Question

if x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 3 ,then what is the value of 4xy?​

Answer 1

The value of 4xy is -8

• It is given that x^2 + xy + y^2 = 3. Now squaring both sides we get x^4+x^2y^2+y^4+2x^3y+2xy^3+2x^2y^2 = 9

• Now x^4+x^2y^2+y^4 = 21 , so 2x^3y+2xy^3+2x^2y^2 = 9-21 = -12

• now taking common 2xy we get 2xy(x^2 + xy + y^2) = -12

• now x^2 + xy + y^2 = 3, so 2xy*3 = 6xy = -12

• hence xy = -12/6 = -2

• Hence the value of 4xy is 4*(-2) = -8

• So the final answer is -8