If X= 1+√2+√3 , then find the value of 2x^4 - 8x^3 + 26x - 28 . Please do it step by step.
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x = 1 + √2 + √3
x - 1 = √2 + √3
On squaring both sides, we get
x2 – 2x + 1 = 2 + 3 + 2√6
x2 – 2x = 4 + 2√6 …(i)
x2 – 2x - 4 = 2√6
on squaring both sides, we get
x4 + 4x2 + 16 – 4x3 + 16x – 8x2 = 24
x4 – 4x3 - 4x2 + 16x – 8 = 0
2x4 – 8x3 - 8x2 + 32x – 16 = 0
2x4 – 8x3 - 5x2 + 26x – 28 = 0
= 3x2 – 6x – 12 = 3(x2 – 2x) – 12
= 3(4 + 2√6) – 12
= 12 + 6√6 – 12 = 6√6
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