Question

(a+b)^-1 × (a^-1 +b^-1) = a^x*b^y. find x and y

Answer 1

Answer :

Given that,

${(a+b)}^{-1}\times({a}^{-1}+{b}^{-1})={a}^{x}\times{b}^{y}\\\\\implies\frac{1}{a+b}\times(\frac{1}{a}+\frac{1}{b})={a}^{x}\times{b}^{y}\\\\\implies\frac{1}{a+b}\times\frac{b+a}{ab}={a}^{x}\times{b}^{y}\\\\\implies\frac{1}{ab}={a}^{x}\times{b}^{y}\\\\\implies{a}^{-1}\times{b}^{-1}={a}^{x}\times{b}^{y}$

Now, comparing among the powers, we get

x = - 1 & y = - 1

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