Question

if x+y varries directly with x-y then show that x^2 + y^ varries directly with xy​

Answer 1

Answer:

Let x = ky then,

x² + y² = k²y² + y² = y² (k² + 1)

x² - y² = k²y² - y² = y² (k² − 1)

So

x² + y²/x² + y² = (k² + 1/k² - 1)

x² + y² = 1(x² - y²) where 1 = (k² + 1/k² - 1) , a

constant.

Hence proved.