Question

if x+y=3 and x^2+y^2=15 then value of
(x-y)^2 will be

Answer 1

=>(x+y)² =x²+y²+2xy
=>3² = 15+2xy
=>2xy = 9-15 = -6
=>xy = -3

=>(x-y)²= (x+y)²-4xy
=>(x-y)²= 3²-4×-3
=>(x-y)²=9+12
=>(x-y)²=21

Answer 2

Here is your answer

x + y = 3

x^2 + y^2 = 15

Now
$(x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ 3 {}^{2} = 15 + 2xy \\ 2xy = 9 - 15 \\ xy = \frac{ - 6}{2} \\ xy = - 3$
Now
$(x - y) {}^{2} = {x}^{2} + {y}^{2} - 2xy \\ (x - y) {}^{2} = 15 - 2( - 3) \\ (x - y) {}^{2} = 15 + 6 \\ (x - y) {}^{2} = 21$
Hope it helps you