Question

If x-y=16 and x2+y2 =400 find xy

Answer 1

Step-by-step explanation:

$given \: x - y = 16 \\ {x}^{2} + {y}^{2} = 400 \\ \: we \: know \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ so \: {(x - y)}^{2} = {x}^{2}+ {y}^{2} - 2xy \\ {16}^{2} = 400 - 2xy \\ 256 - 400 = -2xy \\ - 144 = - 2xy \\ xy = \frac{ - 144}{ - 2} \\ xy = 72$

This may help you

Answer 2

Answer:

givenx−y=16

x

2

+y

2

=400

weknow(x−y)

2

=x

2

−2xy+y

2

so(x−y)

2

=x

2

+y

2

−2xy

16

2

=400−2xy

256−400=−2xy

−144=−2xy

xy=

−2

−144

xy=72