Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 n n n 2 n b 2b c c n n n n ac 2b c bd Using 1 and 2 n n n n n n n n a c b c b c b d n n n n n n n n a c b c a d b d [Using (3)] n n n n n n c a b d a b n n n n a b c d R.H.S 2 b n c n a n b n c n d n Thus, , and a b , b c n n n n c n d n are in G.P. Question 18: If a and b are the roots of 2 x x p 3 0 form a G.P. Prove that Solution 18: It is given that a a b 3 Also, c c d 12 and It is given that Let and q p : q p 17 :15 and b are the roots of ab p ....... 1 and d are the roots of and cd q a, b, c, d are in G.P. a x, b xr, c xr , d xr From (1) and (2), 2 3 We obtain x xr x r xr xr 12 2 3 xr 2 1 r 12 On dividing, we obtain r xr 2 1 12 x 1 r 3 2 r 4 r 2 When 3 1 3 3 3 r 2, x 1 1 2 3 2 x x q cd , . 2 x x p 12 0 ...... 2 3 0 are roots of 2 x x q 12 0 , where a, b, c, d Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ When 3 3 r 2, x 3 12 1 Case I: When r 2 and q p 32 2 34 17 q p 32 2 30 15 q p : q p 17 :15 i.e., Case II: When x ab x r cd x r 2 2 5 1, 2 32 r x ab x r cd x r 2 2 5 2, 3, 18, 288 q p 288 18 306 17 q p 288 18 270 15 q p : q p 17 :15 i.e., q p : q p 17 :15 Thus, in both the cases, we obtain . Question 19: The ratio of the A.M and G.M. of two positive numbers a 2 2 2 2 a : b m m n : m m n Solution 19: Let the two numbers be a and b A.M a b 2 and G.M. ab According to the given condition, a b m 2 ab n 2 a b m 4 ab n 2 4abm a b 2 n 2 2 2 a b 1 2 abm n Using this in the identity 2 2 4abm 4ab m a b 4ab n n 2 2 . 2 2 a b a b 4 ab, we obtain n 2 2 and b , is m: n . Show that Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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