First slide

Types of real valued functions XI

Question

If $\log_{y} x + \log_{x} y = 2, x^{2} + y = 12$ then the value of xy is

Moderate

A

9
B

12
C

15
D

21

Solution

$\log_{y} (x) = t \Rightarrow t + 1 / t = 2 \Rightarrow t = 1 \Rightarrow x = y$
$x^{2} + x - 12 = 0 \Rightarrow x = 3, x = - 4 n o t p o s s i b l e$
x=y=3

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