Question

if x²+y²=10 and xy=4,find the value of (x-y)²​

Answer 1

Step-by-step explanation:

Given ,x^2+y^2=10, xy = 4,

(x^2+y^2)^2 = 10^2 = 100.

or x^4 + 2(x^2)(y^2) + y^4 = 100.

Now, (x+y)^4 = x^4+4(x^3)y + 6(x^2)(y^2) + 4xy^3 + y^4

= [x^4 + 2(x^2)(y^2) + y^4] + [4(x^3)y + 4(x^2)(y^2) + 4xy^3]

=100 + 4[(x^3)y + (x^2)(y^2) + xy^3]

= 100 + 4xy[x^2 + xy + y^2]

= 100 + 4*4[10+4]

= 100 + 16*14

= 100 + 224

= 324