Question

${5}^{x + y} = 125 \\ {5}^{x - y} = 25$
Find the values of x and y.

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

${5}^{x + y} = {5}^{x} .5y = 125 \\ {5}^{x} = \frac{125}{ {5}^{y} }$

${5}^{x - y} = \frac{ {5}^{x} }{ {5}^{y} } = 25 \\ \frac{ \frac{125}{ {5}^{y} } }{ {5}^{y} } = 25$

let

${5}^{y} = t$

then

$\frac{ \frac{125}{ {t}} }{t} = 25 \\ \frac{125}{ {t}^{2} } = 25 \\ {t}^{2} = \frac{125}{25} = 25 \\ so \: t = + _{ - }25$

now

${5}^{y} = 25 = {5}^{2 } \\ so \: y = 2$

and

${5}^{x} = \frac{125}{ {5}^{y} } = \frac{125}{25 } \\ = 25 = {5}^{2} = so \: x = 2$

now we can say that x= y=2 ans