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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Find all real solutions of x4−5x2+4=0x^4 - 5x^2 + 4 = 0.

  • A

    x=±1,±2x = \pm 1, \pm 2

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  • B

    x=1,4x = 1, 4

  • C

    x=±2x = \pm 2

  • D

    x=±1,±4x = \pm 1, \pm 4

Explanation

Let u=x2u = x^2: u2−5u+4=(u−1)(u−4)=0u^2 - 5u + 4 = (u-1)(u-4) = 0, so x2=1x^2 = 1 or x2=4x^2 = 4. Hence x=±1,±2x = \pm 1, \pm 2.

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