{"id":17649,"date":"2023-01-16T16:44:29","date_gmt":"2023-01-16T11:14:29","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=17649"},"modified":"2023-03-29T15:53:08","modified_gmt":"2023-03-29T10:23:08","slug":"ap-board-10th-class-maths-solutions-chapter-1-optional-exercise-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/ap-board-10th-class-maths-solutions-chapter-1-optional-exercise-in-telugu\/","title":{"rendered":"AP Board 10th Class Maths Solutions Chapter 1 \u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41 Optional Exercise"},"content":{"rendered":"

SCERT AP 10th Class Maths Textbook Solutions<\/a> Chapter 1 \u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41 Optional Exercise Textbook Exercise Questions and Answers.<\/p>\n

AP State Syllabus 10th Class Maths Solutions 1st Lesson \u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41 Optional Exercise<\/h2>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\nn \u0c12\u0c15 \u0c38\u0c39\u0c1c \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c17\u0c3e \u0c15\u0c32\u0c3f\u0c17\u0c3f\u0c28 \u0c38\u0c02\u0c16\u0c4d\u0c2f 6n<\/sup> \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c12\u0c15\u0c1f\u0c4d\u0c32 \u0c38\u0c4d\u0c25\u0c3e\u0c28\u0c02\u0c32\u0c4b 5 \u0c09\u0c02\u0c1f\u0c41\u0c02\u0c26\u0c3e ? \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n6n<\/sup> = (2 \u00d7 3)n<\/sup> = 2n<\/sup> \u00d7 3n<\/sup>
\n6n<\/sup> \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c12\u0c15\u0c1f\u0c4d\u0c32 \u0c38\u0c4d\u0c25\u0c3e\u0c28\u0c02\u0c32\u0c4b 5 \u0c09\u0c02\u0c21\u0c26\u0c41.
\n\u0c15\u0c3e\u0c30\u0c23\u0c02:
\nn \u0c12\u0c15 \u0c38\u0c39\u0c1c \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c2f\u0c3f\u0c28 6n<\/sup> \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c2a\u0c4d\u0c30\u0c27\u0c3e\u0c28 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c32\u0c4b 5 \u0c32\u0c47\u0c26\u0c41.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 2.
\n7 \u00d7 5 \u00d7 3 \u00d7 2 + 3 \u0c05\u0c28\u0c47\u0c26\u0c3f \u0c38\u0c02\u0c2f\u0c41\u0c15\u0c4d\u0c24 \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c17\u0c41\u0c28\u0c3e? \u0c28\u0c40 \u0c1c\u0c35\u0c3e\u0c2c\u0c41\u0c28\u0c41 \u0c38\u0c2e\u0c30\u0c4d\u0c25\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n7 \u00d7 5 \u00d7 3 \u00d7 2 + 3 = 3 (7 \u00d7 5 \u00d7 2 + 1)
\n= 3 \u00d7 (70 + 1)
\n= 3 \u00d7 71
\n7 \u00d7 5 \u00d7 3 \u00d7 2 + 3 \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 3 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 71. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c38\u0c02\u0c2f\u0c41\u0c15\u0c4d\u0c24 \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c35\u0c41\u0c24\u0c41\u0c02\u0c26\u0c3f.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 3.
\n2\u221a3 + \u221a5 \u0c12\u0c15 \u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c28\u0c3f \u0c28\u0c3f\u0c30\u0c42\u0c2a\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f. \u0c07\u0c26\u0c47\u0c35\u0c3f\u0c27\u0c02\u0c17\u0c3e (2\u221a3 + \u221a5) (2\u221a3 – \u221a5) \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c2e\u0c17\u0c41\u0c28\u0c4b, \u0c15\u0c30\u0c23\u0c40\u0c2f\u0c2e\u0c17\u0c41\u0c28\u0c4b \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n(i) 2\u221a3 + \u221a5 = x, x, \u0c12\u0c15 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c28\u0c41\u0c15\u0c41\u0c02\u0c26\u0c3e\u0c2e\u0c41.
\n2\u221a3 = x – \u221a5
\n\u0c07\u0c30\u0c41\u0c35\u0c48\u0c2a\u0c41\u0c32\u0c3e \u0c35\u0c30\u0c4d\u0c17\u0c02 \u0c1a\u0c47\u0c2f\u0c17\u0c3e,
\n(2\u221a3)2<\/sup> = (x – \u221a5)2<\/sup>
\n12 = x2<\/sup> – 2\u221a5 x +5
\n2\u221a5x = x2<\/sup> + 5 -12
\n\u221a5 = \\(\\frac{x^{2}-7}{2 x}\\)
\nx \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c2f\u0c3f\u0c24\u0c47 \\(\\frac{x^{2}-7}{2 x}\\) \u0c12\u0c15 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c15\u0c3e\u0c35\u0c41\u0c28 \u221a5 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f. \u0c07\u0c26\u0c3f \u221a5 \u0c12\u0c15 \u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c15\u0c41 \u0c35\u0c3f\u0c30\u0c41\u0c26\u0c4d\u0c27\u0c2e\u0c41. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c2e\u0c28 \u0c0a\u0c39 2\u221a3 + \u221a5 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c28\u0c21\u0c02 \u0c35\u0c3f\u0c30\u0c4b\u0c27\u0c3e\u0c2d\u0c3e\u0c38\u0c02.
\n\u2234 2\u221a3 + \u221a5 \u0c12\u0c15 \u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f.<\/p>\n

(ii) (2\u221a3 + \u221a5) (2\u221a3 – \u221a5)
\n= (2\u221a3) – (\u221a5)
\n= 12 – 5 = 7
\n\u0c12\u0c15 \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c15\u0c3e\u0c35\u0c41\u0c28 (2\u221a3 + \u221a5) (2\u221a3 – \u221a5) \u0c05\u0c15\u0c30\u0c23\u0c40\u0c2f \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c35\u0c41\u0c24\u0c41\u0c02\u0c26\u0c3f.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 4.
\nx2<\/sup> + y2<\/sup> = 6xy \u0c05\u0c2f\u0c3f\u0c28 2 log (x + y) = log x + log y + 3 log 2 \u0c05\u0c28\u0c3f \u0c1a\u0c42\u0c2a\u0c02\u0c21\u0c3f.
\n\u0c27\u0c28.
\nx2<\/sup> + y2<\/sup> = 6xy
\nx2<\/sup> + y2<\/sup> + 2xy = 6xy + 2xy
\n(x + y)2<\/sup> = 8xy
\n\u0c07\u0c30\u0c41\u0c35\u0c48\u0c2a\u0c41\u0c32\u0c3e log \u0c24\u0c40\u0c38\u0c41\u0c15\u0c4a\u0c28\u0c17\u0c3e
\nlog (x + y)2<\/sup> = log 8xy
\n2 log(x + y) = log 8 + log x + log y
\n[\u2235 log xm<\/sup> = m log x]
\n[\u2235 log xy = log x + log y]
\n= log 23<\/sup> + log x + log y
\n= 3 log 2 + log x + log y
\n\u2234 2 log(x + y)= log x + log y + 3 log 2<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 5.
\nlog10<\/sub> 2 = 0.3010 \u0c05\u0c2f\u0c3f\u0c28 42013<\/sup> \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c4b \u0c0e\u0c28\u0c4d\u0c28\u0c3f \u0c05\u0c02\u0c15\u0c46\u0c32\u0c41\u0c02\u0c1f\u0c3e\u0c2f\u0c4b \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\nx = 42013<\/sup> \u0c05\u0c28\u0c41\u0c15\u0c41\u0c02\u0c26\u0c3e\u0c2e\u0c41
\nlog x = log 42013<\/sup>
\n= log (22<\/sup>)2013<\/sup>
\n= log 24026<\/sup>
\n= 4026 log 2 [\u2235 log xm<\/sup> = m logy)
\n= 4026 \u00d7 0.3010 [ log 2 = 0.3010]
\nlog x = 1211.826
\nlog x \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c32\u0c3e\u0c15\u0c4d\u0c37\u0c23\u0c3f\u0c15 (\u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c3e\u0c02\u0c15\u0c2d\u0c3e\u0c17\u0c02) 1211.
\n\u0c15\u0c3e\u0c35\u0c41\u0c28 X \u0c32\u0c4b 1211 + 1 = 1212 \u0c05\u0c02\u0c15\u0c46\u0c32\u0c41\u0c02\u0c1f\u0c3e\u0c2f\u0c3f.
\n\u2234 42013<\/sup> \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c4b 1212 \u0c05\u0c02\u0c15\u0c46\u0c32\u0c41\u0c02\u0c1f\u0c3e\u0c2f\u0c3f.
\n\u0c38\u0c42\u0c1a\u0c28 :
\n\u0c12\u0c15 \u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c38\u0c02\u0c35\u0c30\u0c4d\u0c17\u0c2e\u0c3e\u0c28\u0c02\u0c32\u0c4b \u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c3e\u0c02\u0c15 \u0c2d\u0c3e\u0c17\u0c02 \u0c17\u0c41\u0c30\u0c3f\u0c02\u0c1a\u0c3f, \u0c26\u0c36\u0c3e\u0c02\u0c36 \u0c2d\u0c3e\u0c17\u0c02 \u0c17\u0c41\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c2e\u0c40 \u0c09\u0c2a\u0c3e\u0c27\u0c4d\u0c2f\u0c3e\u0c2f\u0c41\u0c21\u0c3f\u0c28\u0c3f \u0c05\u0c21\u0c3f\u0c17\u0c3f \u0c24\u0c46\u0c32\u0c41\u0c38\u0c41\u0c15\u0c4b\u0c02\u0c21\u0c3f.<\/p>\n","protected":false},"excerpt":{"rendered":"

SCERT AP 10th Class Maths Textbook Solutions Chapter 1 \u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41 Optional Exercise Textbook Exercise Questions and Answers. AP State Syllabus 10th Class Maths Solutions 1st Lesson \u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41 Optional Exercise \u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1. n \u0c12\u0c15 \u0c38\u0c39\u0c1c \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c17\u0c3e \u0c15\u0c32\u0c3f\u0c17\u0c3f\u0c28 \u0c38\u0c02\u0c16\u0c4d\u0c2f 6n \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c12\u0c15\u0c1f\u0c4d\u0c32 \u0c38\u0c4d\u0c25\u0c3e\u0c28\u0c02\u0c32\u0c4b 5 \u0c09\u0c02\u0c1f\u0c41\u0c02\u0c26\u0c3e ? \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f. \u0c38\u0c3e\u0c27\u0c28. 6n = (2 \u00d7 3)n = … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":35285,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/apboardsolutions.com\/wp-content\/uploads\/2023\/01\/Chapter-1-\u0c35\u0c3e\u0c38\u0c4d\u0c24\u0c35-\u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41-Optional-Exercise-1.png","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17649"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=17649"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17649\/revisions"}],"predecessor-version":[{"id":17650,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17649\/revisions\/17650"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media\/35285"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=17649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=17649"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=17649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}