Question

Find the value of x cubed minus 2x squared minus 7x + 5 of x=1/2-√3 ​

Answer 1

9514 1404 393

Answer:

  3

Step-by-step explanation:

For f(x) = x^3 -2x^2 -7x +5 and x=1/(2-√3), we have ...

  f(x) = ((x -2)x -7)x +5

and ...

  x = 1/(2-√3) = (2+√3)/(2^2 -3) = 2+√3

Then ...

  f(2+√3) = ((2 +√3 -2)(2 +√3) -7)(2 +√3) +5

  = (3+2√3 -7)(2+√3) +5

  = 2(√3 -2)(√3 +2) +5 = 2(3 -4) +5 = -2 +5

  f(1/(2 -√3)) = 3

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If you really mean x = (1/2) -√3, then f(x) = (42√3 -3)/8.