Theory of Intelligence
A-LEVEL•Mathematics•Quadratics•Question 4

Solution

🟢 Foundation · [4 marks] Solve the equation $x^4 - 10x^2 + 9 = 0$.

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Solution

Let u=x2u = x^2:

u2−10u+9=0(u−1)(u−9)=0u=1oru=9\begin{aligned} u^2 - 10u + 9 &= 0 \\ (u - 1)(u - 9) &= 0 \\ u = 1 \quad&\text{or}\quad u = 9 \end{aligned}

Convert back: x2=1x^2 = 1 gives x=±1x = \pm 1, and x2=9x^2 = 9 gives x=±3x = \pm 3.

x=−3, −1, 1, 3x = -3,\ -1,\ 1,\ 3

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