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If $4 x^4=5 x^2-1, x>\frac{1}{\sqrt{2}}$, then what is the value of $\left(2 x^2-x-1\right)$ ? |
1 -2 0 2 |
0 |
4x4 - 5x2 + 1 = 0 = 4x4 - 4x2 - x2 + 1 = 0 = 4x2(x2 - 1) – 1(x2 - 1) = 0 = (x2 - 1)(4x2 – 1) = 0 = (x2 - 1) = 0 (4x2 – 1) = 0 x - 1 = 0 2x – 1 = 0 x = 1 another value of x = \(\frac{1}{2}\) (2x2 - x - 1) Put x = 1 2 × 1 - 1 - 1 = 2 - 2 = 0 |
