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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

Solve: x+7−x−1=2\sqrt{x+7} - \sqrt{x-1} = 2.

  • A

    x=1x = 1

  • B

    x=2x = 2

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  • C

    x=9x = 9

  • D

    x=5x = 5

Explanation

x+7=2+x−1\sqrt{x+7} = 2 + \sqrt{x-1}. Square: x+7=4+4x−1+x−1⇒4=4x−1⇒x−1=1⇒x=2x + 7 = 4 + 4\sqrt{x-1} + x - 1 \Rightarrow 4 = 4\sqrt{x-1} \Rightarrow \sqrt{x-1} = 1 \Rightarrow x = 2.

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