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Biquadric Radical Revelations (
Posted on 2024-08-22
)
If x=√2+√3+√6 is a root of x
4
+ax
3
+bx
2
+cx+d=0 where a, b, c, d are integers. What is the value of |a+b+c+d|?
No Solution Yet
Submitted by
Danish Ahmed Khan
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Solution
Comment 1 of 1
x=√2+√3+√6
x-
√6
=√2+√3
x^2 - 2xsqrt6 + 6 = 2 + 2sqrt6 + 3
x^2 + 1 = (2x + 2)sqrt6
x^4 + 2x^2 + 1 = 24(x^2 + 2x + 1)
x^4 - 22x^2 - 48x -23 = 0
So |a+b+c+d|=0+-22+-48+-23| = 93
Posted by
Jer
on 2024-08-22 14:25:56
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