heshamelaziry wrote:If x^6 - y^6 = 0 then what is the value of x^3 - y^3 ?
(1) xy > 0
(2) x = 2
Statement 1
This is another Magoosh question.
Here, it first helps to take the equation x^6-y^6=0 and factor it to get:
(x^3+y^3)(x^3-y^3)=0
So, we that either x^3+y^3=0 or x^3-y^3=0
Statement(1) essentially tells us that x^3+y^3 does NOT equal zero. If xy>0, then there are two possible cases:
case a) x and y are both positive, in which case x^3 is positve and y^3 is positive. If x^3 and y^3 are both positive, then x^3+y^3 will be positive. In other words, x^3+y^3 does not equal zero, in which case x^3-y^3 must equal zero.
case b) x and y are both negative, in which case x^3 is negative and y^3 is negative . . . (same line of reasoning as above) . . . then x^3+y^3 will be negative. In other words, x^3+y^3 does not equal zero, in which case x^3-y^3 must equal zero.
In both cases, x^3-y^3 must equal zero (SUFFICIENT)
(2) x=2 --> y=2, or -2.
When x=2 and y=2, x^3-y^3=0
When x=2 and y=-2, then x^3-y^3=16
INSUFFICIENT
