Algebra

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If x = 1 /√5 – 2 than x⁴ + 16x² – 8x³ = ?

-5

–2 √5

√5 + 2

Explanation:

x = 1/√5 – 2
x = √5 + 2
x – 2 = √5
x² – 4x + 4 = 5
x² – 4x – 1 = 0 .........(i)
x² – 4x + 1 = 2 ..........(ii)
Multiply eq. (i) by eq. (ii)
(x² – 4x – 1) (x² – 4x + 1) = 0
(x² – 4x)² – 1 = 0
x⁴ + 16x² – 8x³ = 1

By: Amit Kumar

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