SOLUTION: Let x be an integer that satisfies x^4 + 24 = 105. What is the value of x^2 − 24?

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Question 725017: Let x be an integer that satisfies x^4 + 24 = 105. What is the value of x^2 − 24?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+%2B+24+=+105
Subtracting 24:
x%5E4+=+81
Finding the 4th root of each side (and remembering that even-numbered roots have a positive and negative root):
x+=+root%284%2C+81%29 or x+=+-root%284%2C+81%29
Since 3%5E4+=+81 these roots are 3's:
x+=+3 or x+=+-3
Now we can find x%5E2-24...
for x = 3:
3%5E2-24+=+9-24+=+-15
for x = -3:
%28-3%29%5E2-24+=+9-24+=+-15
So x%5E2-24+=+-15