Ex 9.3, 25 - Chapter 9 Class 11 Sequences and Series (Term 1)
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Ex9.3,25 If a, b, c and d are in G.P. show that . (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 We know that a, ar , ar2 , ar3, …. are in G.P. with first term a & common ratio r Given a, b, c, d are in G.P. So, a = a b = ar c = ar2 d = ar3 We need to show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 Taking L.H.S (a2 + b2 + c2) (b2 + c2 + d2) Putting values of b = ar , c = ar2 , d = ar3 (a2 + (ar)2 + (ar2)2) ((ar)2 + (ar2)2 + (ar3)2) = (a2 + a2r2 + a2r4) (a2r2 + a2r2 + a2r6) = ["a2(1 + r2 + r4)" ] ["a2r2(1 + r2 + r4)" ] = ["a2" ] ["a2r2" ]"(1 + r2 + r4)" "(1 + r2 + r4)" = ["a2 a2 r2" ]"(1 + r2 + r4)"2 = ["a4 r2" ]"(1 + r2 + r4)"2 = "a4 r2(1 + r2 + r4)"2 Taking R.H.S (ab + bc + cd)2 Putting values of b = ar , c = ar2 , d = ar3 = ( a × ar + ar × ar2 + ar2 × ar3) 2 = ( a2r + a2r3 + a2r5 )2 = ["a2r (1 + r2 + r4)" ]^2 = (a2r)2 (1 + r2 + r4)2 = a4r2 (1 + r2 + r4)2 = L.H.S Thus L.H.S = R.H.S Hence proved
Ex 9.3
Ex 9.3, 2
Ex 9.3, 3 Important
Ex 9.3, 4
Ex 9.3, 5 (a)
Ex 9.3, 5 (b) Important
Ex 9.3, 5 (c)
Ex 9.3, 6
Ex 9.3, 7 Important
Ex 9.3, 8
Ex 9.3, 9 Important
Ex 9.3, 10
Ex 9.3, 11 Important
Ex 9.3, 12
Ex 9.3, 13
Ex 9.3, 14 Important
Ex 9.3, 15
Ex 9.3, 16 Important
Ex 9.3, 17 Important
Ex 9.3, 18 Important
Ex 9.3, 19
Ex 9.3, 20
Ex 9.3, 21
Ex 9.3, 22 Important
Ex 9.3, 23 Important
Ex 9.3, 24
Ex 9.3, 25 You are here
Ex 9.3, 26 Important
Ex 9.3, 27 Important
Ex 9.3, 28
Ex 9.3, 29 Important
Ex 9.3, 30 Important
Ex 9.3, 31
Ex 9.3, 32 Important
Ex 9.3
About the Author