Question

If x + y = 18 and x y = 72, what is the value of (x)2 + (y)2 :
A. 120
B. 90
C. 1800
D. cannot be determined​

Answer 1

Answer:

180

x+y=18,xy=72

squaring on both sides

(x+y)²=(18)²

x²+y²+2xy=324

x²+y²+2(72)=324

x²+y²+144=324

x²+y²=324-144

x²+y²=180

Answer 2

Answer:

$x + y = 18 \\ \\ xy = 72$

We know that,

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ {18}^{2} = {x}^{2} + {y}^{2} + 2 \times 72$

Then,

$324 = {x}^{2} + {y}^{2} + 144$

Now,

${x}^{2} + {y}^{2} = 324 - 144 \\ \\ {x}^{2} + {y}^{2} = 180$

Hence, the correct answer is 180.