Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Solution:
First, solve the given equation:
x4 – 25×2 = -144
x4 – 25×2 + 144 = 0
Substitute z = x2:
z2 – 25z + 144 = 0
Use trial and error to find a pair of factors of 144 that sum to 25. Start with 12 & 12, which sum to 24; then try 16 and 9, which work.
(z – 16)(z – 9) = 0
z = 16 or z = 9
Now put x2 back in:
x2 = 16 or x2 = 9
x = -4 or 4, or x = -3 or 3. There are four possible solutions.
Possible sums of two solutions include the following:
-7 = -4 + -3
-1 = -4 + 3
0 = -4 + 4 or -3 + 3
7 = 4 + 3
However, 3 itself is NOT a possible sum of two solutions of the equation.
The correct answer is D.