Question

If x + y = 20 and xy = 84, then (x)^2 + (y)^2 = ? (a) 232 (b) 400 (c) 128 (d) Cannot be determined (e) None of these

Answer 1

x+y = 20 xy = 84
x^2+y^2=?
(x+y)^2 = x^2 +y^2 +2xy
x^2+y^2=(x+y)^2-2xy
=(20)^2 -2×84
=400-168
=232

Answer 2

(x + y)² = x² + 2xy + y²

Take away 2xy from both sides:

(x + y)² - 2xy = x² + y²

Switch sides:

x² + y² = (x + y)² - 2xy

Substitute (x + y)= 20 and xy = 84 into the equation:

x² + y² = (20)² - 2(84)

x² + y² = 400 - 168

x² + y² = 232

Answer: (a) 232