Question

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${2}^{x + y} \times {3}^{x - y} = \sqrt{8} \\ then \: the \: value \: of \: y \: is \: \\ a) \frac{1}{2} \: \: \: \: \: \: b) \frac{3}{2} \: \: \: \: c)0 \: \: \: d ) \: none \: of \: these$
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Answer 1

Step-by-step explanation:

$\mathtt\red{ \implies {2}^{x + y} = {2}^{x - y} = {2}^{ \frac{3}{2} } }$

$\mathtt\red{ \implies \: x + y = \frac{3}{2} \: \: \: \: \: \: \: .(i) }$

$\mathtt\red{ \implies \: and \: x - y = \frac{3}{2} \: \: \: \: .. (ii) }$

$\mathtt\red{on \: solving \: eq(i) \: and \: eq(ii).we \: get}$

$\mathtt\red{x = \frac{3}{2} \: and \: y = 0}$

hope it helpful for you.

thanks.