

Get live Maths 1-on-1 Classs - Class 6 to 12
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
Last updated at March 16, 2023 by Teachoo
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