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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

If rr and ss are roots of x2−4x+1=0x^2 - 4x + 1 = 0, find r3+s3r^3 + s^3.

  • A

    5252

    check_circle
  • B

    6464

  • C

    4848

  • D

    6060

Explanation

r+s=4r+s = 4, rs=1rs = 1. r3+s3=(r+s)3−3rs(r+s)=64−12=52r^3 + s^3 = (r+s)^3 - 3rs(r+s) = 64 - 12 = 52.

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