SOLUTION: What is the sum of the squares of the roots of x^4 - 5 x^2 + 6 = 0

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Question 252245: What is the sum of the squares of the roots of x^4 - 5 x^2 + 6 = 0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
solving the equation:
x%5E4+-+5+x%5E2+%2B+6+=+0
Let z+=+x%5E2
+z%5E2+-+5z+%2B+6+=+0+
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-5
c+=+6
z+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+
z+=+%285+%2B-+sqrt%2825+-+24+%29%29%2F2+
z+=+%285+%2B+1%29%2F2
z+=+3
and
z+=+%285+-+1%29%2F2
z+=+2
--------------------------
Substituting:
x%5E2+=+3
x+=+sqrt%283%29
x+=+-sqrt%283%29
x%5E2+=+2
x+=+sqrt%282%29
x+=+-sqrt%282%29
The sum of the squares of the roots is:
3+%2B+3+%2B+2+%2B+2+=+10