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
Answers
Answered by
7
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
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
Answered by
8
(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
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