Question

If 〖(x+y)〗^(-1)×(x^(-1)+y^(-1) )=x^p y^q,prove that p+q+2=0

Answer 1

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Answer 2

Step-by-step explanation:

The given expression is

$(x+y)^{-1}.(x^{-1} +y^{-1} )=x^{p} y^{q}$

To solve the expression  we have to solve left hand side of the expression first.

$(x+y)^{-1}.(x^{-1} +y^{-1} )$

⇒$\frac{1}{x+y} .(\frac{1}{x} +\frac{1}{y} )$

⇒$\frac{1}{x+y} .(\frac{x+y}{xy} )$

⇒$\frac{1}{xy}$

⇒$x^{-1} y^{-1}$

Now bringing right hand side expression, we get

$x^{-1} y^{-1}=x^{p} y^{q}$

From the above expression it can be said that ,

p=-1 and q=-1

Now putting the value of p and q in the expression needed to prove

$p+q+2=0$

$(-1)+(-1)+2=0$

$-2+2=0$

0=0

Hence Proved

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