Question

x×x+y×y=37,xy=6;find (X+Y) AND (X-Y)

Answer 1

(x+y)=√(x+y)^2
=√(x^2+y^2+2xy)
=√(37+12)
=√49
x+y=7

(x-y)=√(x-y) ^2
=√(x^2+y^2-2xy)
=√(37-12)
=√25
x-y=25

Answer 2

2x+2y=37
x+y=37/2
squaring in both sides
(x+y)^2=(37/2)^2
(x-y)^2+4xy=(37/2)^2
(x-y)^2+4(6)=(37/2)^2
(x-y)^2=(37/2)^2-24
=1369/4-24
=1273/4
=
$x - y = \frac{ \sqrt{1273} }{2}$
hope it helps.....