If α 2 n α 2 n + 2 α 2 n + 4 β 2 n β 2 n + 2 β 2 n + 4 γ 2 n γ 2 n + 2 γ 2 n + 4 = 1 β 2 - 1 α 2 1 γ 2 - 1 β 2 1 α 2 - 1 γ 2 {where α 2 , β 2 and γ 2 are all distinct}, then the value of n is equal to

Question

If α 2 n α 2 n + 2 α 2 n + 4 β 2 n β 2 n + 2 β 2 n + 4 γ 2 n γ 2 n + 2 γ 2 n + 4 = 1 β 2 - 1 α 2 1 γ 2 - 1 β 2 1 α 2 - 1 γ 2 {where α 2 , β 2 and γ 2 are all distinct}, then the value of n is equal to, 4, - 4, 3, - 2

MARKS App · Accepted Answer

Given, α 2 n β 2 n γ 2 n 1 α 2 α 4 1 β 2 β 4 1 γ 2 γ 4 = α 2 - β 2 β 2 - γ 2 ( γ 2 - α 2 ) α 4 β 4 γ 4 ⇒ α 2 n β 2 n γ 2 n [ α 2 - β 2 β 2 - γ 2 γ 2 - α 2 ] = α 2 - β 2 β 2 - γ 2 ( γ 2 - α 2 ) α β γ 4 On comparison, we get, n = - 2

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