Question

If (x+y) : (x-y)=4:1, then (x2+y2):(x2-y2)=?

Answer 1

(x+y)/(x-y) = 4/1

(x+y) = 4(x-y)

(x+y) = 4x-4y

4x-x = y+4y

3x = 5y

x/y = 5/3

(x²+y²)/(x²-y²) = {(x/y)² + 1}/{(x/y)² - 1}

= (5/3)²+1/(5/3)²-1

= 25/9 + 1 / 25/9 - 1

= (34/9) / (16/9)

= 34/16

= 17/8

(x²+y²) : (x²-y²) = 17 : 8

Answer 2

Answer:

17 / 18

Step-by-step explanation:

$\frac{x+y}{x-y} = \frac{4}{1}$  (cross Multiply)

=> 1 (x + y) = 4 (x-y)

=> x + y = 4x - 4y

=> 4y + y = 4x - x

=> 5y = 3x

=> y = 3x / 5

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

=> $\frac{x^{2} + (3x/5)^{2} }{x^{2} - (3x/5)^{2} }$

=> $\frac{x^{2} + 9x^{2} / 25 }{x^{2} - 9x^{2} / 25}$

=> $\frac{34x^{2} / 25 }{16x^{2} / 25}$

=> 34 / 16

=> 17 / 8