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Product Law

If 2x + y =...

Question

If $2 x + y = 3$ and $x y = 1$ , the value of $(x + y)^{x - y}$ is

100

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Solution

The correct option is C $1$
Given $2 x + y = 3$ . and $x y = 1 \Rightarrow y = 1 / x$

$\Rightarrow 2 x + (1 / x) = 3$

$\Rightarrow 2 x^{2} - 3 x + 1 = 0$

$\Rightarrow 2 x^{2} - 2 x - x + 1 = 0$

$\Rightarrow 2 x (x - 1) - 1 (x - 1) = 0$

$\Rightarrow (2 x - 1) (x - 1) = 0$

$\Rightarrow x = 1 / 2$ or $x = 1$

$\Rightarrow y = 2$ or $y = 1$

If $x = 1 / 2$ and $y = 1$ $\Rightarrow (x + y)^{(x - y)} = (3 / 2)^{- 1 / 2}$

If $x = 1$ and $y = 1$ $\Rightarrow (x + y)^{(x - y)} = 2^{0} = 1$

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