Question

If xsq.+ysq.=29 and xy=2 find
1)x+y
2)x-y
3)x raise to power4+y raise to power 4

Answer 1

x^2+y^2=29
xy=2
by using formula (x+y)^2 we get x^2+y^2+2xy
we put the values of x^2+y^2 and xy in the expanded form of formula
1) (x+y)^2=29+2*2
(x+y)^2=33
x+y=square root 33
2) (x-y)^2=x^2+y^2-2xy
(x-y)^2=29-2*2
(x-y)^2=25
x-y=5
3) x^4+y^4 can be calculated by squaring x^2+y^2
(x^2+y^2)^2=x^4+y^4+2xy
29^2=x^4+y^4+4
841-4=x^4+y^4
x^4+y^4=837