First slide

Types of real valued functions XI

Question

If $\log_{y} x + \log_{x} y = 2, x^{2} + y = 12$

Moderate

A

9
B

12
C

15
D

21

Solution

$\begin{array}{l} Let t = \log_{y} x (x, y > 0, and \neq 1), then t + \frac{1}{t} = 2 or (t - 1)^{2} = 0 \\ ∴ t = \log_{y} x = 1, i.e., x = y . We get \\ \begin{aligned} x^{2} + x - 12 = 0 x = - 4, 3 \\ x = 3 only (- 4 rejected) \\ ∴ & y = 3 \\ ∴ & x = 9 \end{aligned} \end{array}$

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