Question

Given that x^2 + y^2 = 48 and xy = 5.5 find the value of (2x-2y)^2

Answer 1

Given, x²+y² = 48 and xy = 5.5

Formula of (a-b)² :-

(a-b)² = a²+b²-(2×a×b)

According to the formula,

(2x-2y)² = 2x²+2y² - (2×2x×2y)

= 2(x²+y²) - 8xy

= (2×48) - (8×5.5)

= 96 - 44

= 52

Hence, the value of (2x-2y)² is 52.