{"id":123,"date":"2021-02-05T10:00:13","date_gmt":"2021-02-05T04:30:13","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=123"},"modified":"2021-02-05T10:35:27","modified_gmt":"2021-02-05T05:05:27","slug":"samacheer-kalvi-10th-maths-chapter-3-ex-3-3","status":"publish","type":"post","link":"https:\/\/samacheerguru.com\/samacheer-kalvi-10th-maths-chapter-3-ex-3-3\/","title":{"rendered":"Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.3"},"content":{"rendered":"

You can Download Samacheer Kalvi 10th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.3<\/h2>\n

10th Maths Exercise 3.3 Samacheer Kalvi Question 1.<\/strong>
\nFind the LCM and GCD for the following and verify that f(x) \u00d7 g(x) = LCM \u00d7 GCD.
\n(i) 21x2<\/sup>y, 35xy2<\/sup>
\n(ii) (x3<\/sup> – 1)(x + 1), x3<\/sup> + 1
\n(ii) (x3<\/sup> – 1) (x + 1), (x3<\/sup> – 1)
\n(iii) (x2<\/sup>y + xy2<\/sup>), (x2<\/sup> + xy)
\nSolution:
\n(i) f(x) = 21x2<\/sup>y = 3 \u00d7 7x2<\/sup>y
\ng(x) = 35xy2<\/sup> = 7 \u00d7 5xy2<\/sup>
\nG.C.D. = 7xy
\nL.C.M. = 7 \u00d7 3 \u00d7 5 \u00d7 x2<\/sup>y2<\/sup> = 105x2<\/sup> \u00d7 y2<\/sup>
\nL.C.M \u00d7 G.C.D = f(x) \u00d7 g(x)
\n105x2<\/sup>y2<\/sup> \u00d7 7xy = 21x2<\/sup>y \u00d7 35xy2<\/sup>
\n735x3<\/sup>y3<\/sup> = 735x3<\/sup>y3<\/sup>
\nHence verified.<\/p>\n

(ii) (x3<\/sup> – 1)(x + 1) = (x – 1)(x2<\/sup> + x + 1)(x + 1)
\nx3<\/sup> + 1 = (x + 1) (x2<\/sup> – x + 1)
\nG.C.D = (x+ 1)
\nL.C.M = (x – 1)(x + 1)(x2<\/sup> + x + 1)(x2<\/sup> – x + 1)
\n\u2234 L.C.M. \u00d7 G.C.D = f(x) \u00d7 g(x)
\n(x – 1)(x + 1)(x2<\/sup> + x + 1) (x2<\/sup> – x + 1) = (x – 1)
\n(x2<\/sup> + x + 1) \u00d7 (x + 1) (x2<\/sup> – x + 1)
\n(x3<\/sup> – 1)(x + 1)(x3<\/sup> + 1) = (x3<\/sup> – 1)(x + 1)(x3<\/sup> + 1)
\n\u2234 Hence verified.<\/p>\n

(iii) f(x) = x2<\/sup>y + xy2<\/sup> = xy(x + y)
\ng(x) = x2<\/sup> + xy = x(x + y)
\nL.C.M. = x y (x + y)
\nG.C.D. = x (x + y)
\nTo verify:
\nL.C.M. \u00d7 G.C.D. = xy(x + y) \u00d7 (x + y)
\n= x2<\/sup>y (x + y)2<\/sup> ……….. (1)
\nf(x) \u00d7 g (x) = (x2<\/sup>y + xy2<\/sup>)(x2<\/sup> + xy)
\n= x2<\/sup>y (x + y)2<\/sup> …………… (2)
\n\u2234 L.C.M. \u00d7 G.C.D = f(x) \u00d7 g{x).
\nHence verified.<\/p>\n

Ex 3.3 Class 10 Samacheer Question 2.<\/strong>
\nFind the LCM of each pair of the following polynomials
\n(i) a2<\/sup> + 4a – 12, a2<\/sup> – 5a + 6 whose GCD is a – 2
\n(ii) x4<\/sup> – 27a3<\/sup>x, (x – 3a)2<\/sup> whose GCD is (x – 3a)
\nSolution:
\n(i) f(x) = a2<\/sup> + 4a – 12 = (a + 6)(a – 2)
\n\"10th<\/p>\n

(ii) f(x) = x4<\/sup> – 27a3<\/sup>x = x(x3<\/sup> – (3a)3<\/sup>)
\ng(x) = (x – 3a)2<\/sup>
\nG.C.D = (x – 3a)
\nL.C.M. \u00d7 G.C.D = f(x) \u00d7 g(x)
\nL. C.M = \\(\\frac{x\\left(x^{3}-(3 a)^{3}\\right) \\times(x-3 a)^{2}}{(x-3 a)}\\)
\nL.C.M = x(x3<\/sup> – (3a)3<\/sup>) . (x – 3a)
\n= x(x – 3a)2<\/sup> (x2<\/sup> + 3ax + 9a2<\/sup>)<\/p>\n

10th Maths Exercise 3.3 Question 3.<\/strong>
\nFind the GCD of each pair of the following polynomials
\n(i) 12(x4<\/sup> – x3<\/sup>), 8(x4<\/sup> – 3x3<\/sup> + 2x2<\/sup>) whose LCM is 24x3<\/sup> (x – 1)(x – 2)
\n(ii) (x3<\/sup> + y3<\/sup>), (x4<\/sup> + x2<\/sup>y2<\/sup> + y4<\/sup>) whose LCM is (x3<\/sup> + y3<\/sup>) (x2<\/sup> + xy + y2<\/sup>)
\nSolution:
\n(i) f(x)= 12(x4<\/sup> – x3<\/sup>)
\ng(x) = 8(x4<\/sup> – 3x3<\/sup> + 2x2<\/sup>)
\nL.C.M = 24x3<\/sup> (x – 1)(x – 2)
\n\"Ex<\/p>\n

(ii) (x3<\/sup> + y3<\/sup>), (x4<\/sup> + x2<\/sup>y2<\/sup> + y4<\/sup>)
\nL.C.M. = (x3<\/sup> + y3<\/sup>)(x2<\/sup> + xy + y2<\/sup>)
\n\"10th<\/p>\n

10th Maths 3.3 Exercise Samacheer Kalvi Question 4.<\/strong>
\nGiven the LCM and GCD of the two polynomials p(x) and q(x) find the unknown polynomial in the following table
\n\"10th
\nSolution:
\n\"10th
\n\"10th<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.3 10th Maths Exercise 3.3 Samacheer Kalvi Question 1. Find the LCM and GCD for the following […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[2],"tags":[],"blocksy_meta":"","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/123"}],"collection":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/comments?post=123"}],"version-history":[{"count":0,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/123\/revisions"}],"wp:attachment":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/media?parent=123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/categories?post=123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/tags?post=123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}