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IPMAT Indore 2022 - QA (SA) Q7 Explanation
December 26, 2024
Explanation:
(72)
Given logx 2y + logy 2x = 1 and y = x^2 - 30
logx 2y + logy 2x = 1
= 1/2 [logx y + logy x] = 1
= logx y + logy x = 2
= logx y + 1/logx y
= 2 [∴logy x = 1/logy x] -------eqn.(1)
We know, if a is a positive number, then a + 1/a = 2, only when a = 1
Applying it in eq. (1), we can say
logx y = 1 or y = x
So putting y = x, in the 2nd given eqn. y = x^2 - 30
we get x = x^2 - 30
x^2 - x - 30 = 0
x^2 + 5x - 6x - 30 = 0
x (x + 5) – 6 (x + 5) = 0
(x + 5) (x - 6)=0
X = -5 or 6
As x cannot be negative number,
∴ x = y = 6
∴ x^2 + y^2 = 6^2 +6^2
= 36 + 36
= 72