Question #cd354

1 Answer
Apr 17, 2017

Two solutions:
1) If x=21.401754250997379791360490255668, then y=1.40175425099137979136049055675.
2) If x=-1.40175425099379791360490255668, then y=-21.401754250991379791360490255668

Explanation:

Assume x>y.

Then, xy = 30 and x-y=20

Isolating x in both equations yield:
x=30/y and x=20+y
By the transitive property, 30/y=20+y.
Multiplying both sides by y, 30=y(20+y), which expands to 30=y^2+20y
Thus, y^2+20y-30=0

By using the quadratic formula, we find that y=(-20+-sqrt(520))/2
Simplifying sqrt(520) gives us 2sqrt(130) and so y may equal (-20+2sqrt(130))/2 or (-20-2sqrt(130))/2.

Simplifying, y may equal -10+-sqrt(130), which turns out to be approximately 1.40175425099137979136049055675 or -21.401754250991379791360490255668

If we substitute each of these values in the equation x-y=20, then we find that x may be (approximately) 21.401754250997379791360490255668 or -1.40175425099379791360490255668.