If a ,   b and c be three distinct real numbers in G.P. and a + b + c = x b , then x cannot be:

If a, b and c be three distinct real numbers in G.P. and a+b+c=xb, then x cannot be:
  1. -3
  2. 2
  3. 4
  4. -2

Solution

Given a, b, c are in G.P.

Let common ratio of G.P. be r , then b=ar, c=ar2

Given equation can be written as

a+ar+ar2=x. a. r

⇒x=r+1r+1

As we know r>0, then r+1r≥2⇒x≥3

r<0, then r+1r≤-2⇒x≤-1

⇒x∈-∞,-1∪3, ∞

Hence, x ≠2.

Asked in: JEE Main 2019 (09 Jan Shift 1)

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