Question

If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,​

Answer 1

x^3+y^3=(x+y)(x^2-xy +y^2)

or, 9=3(x^2-xy+y^2)

or, x^2-xy +y^2=3

or, x^2+y^2=3+xy ....(1)

Again (x+y)^2=3^2=9

or x^2+y^2=9-2xy........(2)

From (1) &(2), 3+xy =9-2xy

or, xy =2

Now x^4+y^4=(x^2+y^2)^2-2.x^2.y^2

=(3+xy)^2-2(xy)^2

=(3+2)^2-2.(2^2)=25-8=17(Ans)