Question

If x+y=12 and xy=32 fine the value of x.x+y.y

Answer 1

(x+y)2= x2 + y2 + 2xy
(12)2 = x2 + y2 + 2(32)
144 = x2 + y2 + 64
144 - 64 = x2 + y2
80 = x2+y2

x2 + y2 = 80. HOPE THIS HELPS

Answer 2

X+y=12-------eqn1
X=12-y

Xy=32 - - - - - - - - - eqn2
Puting value of x in eqn2
(12-y)y=32
12y-y^2-32=0
Y^2-12y+32=0
Y^2-8y-4y+32=0
Y(y-8)-4(y-8)=0
(y-8)(y-4)=0
Either, y =8 or 4
So,
X =12-y=12-8=4
Or,12-4=8

Now,
X.x+y.y
=4.4+8.8=80
or,
X.x+y.y
=8.8+4.4
=80

Hope it helps!