The sum of two positive numbers is 20% of the sum of theirsquares

The sum of two positive numbers is 20% of the sum of their
squares and 25% of the difference of their squares. If the numbers are x and y then,
x + y is equal to
x²

According to the question,

x + y = (x² + y²) ×	1
	5

Again, x + y = (x² + y²) ×	1
	4

∴	x² + y²	=	x² - y²
	5		4

⇒ 5x² – 5y² = 4x² + 4y²
⇒ 5x² – 4x² = 5y² + 4y²
⇒ x² = 9y²
⇒ x = 3y

∴	x + y	=	x² + y²
	x²		5x²

=	9y² + y²	=	10y²	=	2
	5 × 9y²		45y²		9

	x + y	is equal to
	x²