Question 74

If $$(2x - y) : (5x + 3y) = 3 : 8$$, then $$(x^2 + y^2) : (x^2 - y^2) =$$

Solution

$$(2x - y) : (5x + 3y) = 3 : 8$$

$$\frac{(2x-y)}{(5x+3y)}\ =\ \frac{3}{8}$$

16x-8y = 15x+9y

16x-15x = 9y+8y

x = 17y

$$\frac{(x^2+y^2)}{(x^2-y^2)}$$ = $$\frac{\left(\left(17y\right)^2+y^2)\right)}{\left(\left(17y\right)^2-y^2)\right)}$$ [putting the value of 'x'.]

= $$\frac{289y^2+y^2}{289y^2-y^2}$$

= $$\frac{290y^2}{288y^2}$$

= $$\frac{145}{144}$$

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