Question

if 5x-13y= 3x-8y, what is the value of x²+y²/x²-y²?
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Answer 1

Answer:

29/21

Step-by-step explanation:

5x-13y=3x-8y

2x=13y-8y

2x=5y

x/y=5/2

x²/y²=5²/2²

x²/y²=25/4

[BY APPLYING COMPONENDO AND DIVIDENDO]

(x²+y²)/(x²-y²)=(25+4)/(25-4)

(x²+y²)/(x²-y²)=29/21

Answer 2

Answer:

The value of the given expression is

$\frac{x^{2}+y^{2} }{x^{2}-y^{2}}=\frac{29}{21}$

Step-by-step explanation:

The given relation between two variables is $5x-13y=3x-8y$ and we are required to find the value of $\frac{x^{2}+y^{2} }{x^{2}-y^{2}}$

First we simplify the relation between two variables as follows

$5x-13y=3x-8y= > 2x=5y= > x=\frac{5y}{2}$

Substituting the value of x in our required expression,we get

$\frac{x^{2}+y^{2} }{x^{2}-y^{2}}\\=\frac{(\frac{5y}{2})^{2}+y^{2} }{(\frac{5y}{2})^{2}-y^{2}} \\=\frac{\frac{25y^{2}+4y^{2}}{4} }{\frac{25y^{2}-4y^{2}}{4} } =\frac{29y^{2}}{21y^{2}} =\frac{29}{21}$

Therefore,the value of the given expression is

$\frac{x^{2}+y^{2} }{x^{2}-y^{2}}=\frac{29}{21}$

#SPJ2