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IPMAT Indore 2022 - QA (SA) Q11 Explanation
December 26, 2024
Explanation:
(3)
If a, b, c are 3 terms in A.P
then a+b/2 = b or, a+c = 2b
So, -16, 2^x+3 - 2^2x−1 - 16, 2^2x−1 + 16 are in A.P.
We can say, -16 + 2^2x−1 +16 = 2 [2^x+3 - 2Y2x-1 -16]
= 2^2x 2−1 = 2^x+4 - 2^2x - 16x2
= 2^2x / 2 = 2^x.2^4 - 2^2x - 32 --------eqn.(1)
put 2^x = t & 2^2x = t^2
the eqn. becomes t^2/2 =16t - t^2 - 32
= t^2= 32t - 2t^2 - 32 × 2
= 3t^2 - 32t + 32 × 2 = 0
= 3t^2−32t + 64 = 0
t = 8 or 8/3
As t = 2^x, it can not be a fraction
∴ t = 2^x = 8 (only)
∴ x = 3