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Biquadric Radical Revelations (Posted on 2024-08-22)

If x=√2+√3+√6 is a root of x⁴+ax³+bx²+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

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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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