Question 1199217: Solve for x.
x^4 - 5x^2 -12 = 0
I can write x^4 like this: (x^2)^2.
Let u = x^2.
u^2 - 5u - 12 = 0
After using the quadratic formula, I got the following:
u = (5 + sqrt{73})/2 and (5 - sqrt{73})/2.
I back-substituted for u.
x^2 = (5 + sqrt{73})/2 and x^2 = (5 - sqrt{73})/2.
Taking the square root on both sides, I got:
x = [(5 + sqrt{73}/2)]^(1/2)
x = [(5 - sqrt{73}/2)]^(1/2)
The textbook Answer for x are -2, -1, 1, 2.
Why is my answer wrong?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
The textbook answers are wrong.
You can easily check them by substituting into your original equation.
Your answers are correct.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The work you did is fine. But if the textbook answers are -2, -1, 1, and 2, then your original polynomial is not right.
It looks as if you started with the wrong polynomial.
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