Question

One of the factors of x²+ y²+ 2xy -z² is
(a) (x - y +z)
(b) (x + y - z)
(c)(-x-y+z)
(d) (- x + y - z)​

Answer 1

Answer:

This is difficult to solve under 5 mins. Is it really gmat like?

Let

a= x+y+z = 2

b= x^2+y^2+z^2 = 6

c= x^3+y^3+z^3 = 8

* d= xy+yz+xz = (a^2-b)/2 = (2^2-6)/2 = -1

* e= xyz = (a^3-3ab+2c)/6 = (2^3-3.2.6+2.8)/6 = -2

* x^4+y^4+z^4

= (x^2+y^2+z^2)^2 - 2{x^2.y^2+y^2.z^2+x^2.z^2}

= (x^2+y^2+z^2)^2 - 2{(xy+yz+xz)^2 - 2xyz(x+y+z)}

= b^2 - 2{d^2-2e.a}

= 36 - 2{1-2(-2).2}

= 36 - 2.9

= 18

FINAL ANSWER IS (C)