SOLUTION: X^4+4x^3+6x^2+4x+9 find the value of this question if x=√-2-1

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Question 984439: X^4+4x^3+6x^2+4x+9 find the value of this question if x=√-2-1
Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!

Notice that

x%5E4+%2B+4x%5E3+%2B+6x%5E2+%2B+4x+%2B+9 = x%5E4+%2B+4x%5E3+%2B+6x%5E2+%2B+4x+%2B+1 + 8 = %28x%2B1%29%5E4 + 8.

Now,   at  x = sqrt%28-2%29-1   you have

x%2B1 = sqrt%28-2%29  and  %28x%2B1%29%5E4 = %28sqrt%28-2%29%29%5E4 = %28-2%29%5E2 = 4.

As a last step,

x%5E4+%2B+4x%5E3+%2B+6x%5E2+%2B+4x+%2B+9 = %28x%2B1%29%5E4 + 8 = 4 + 8 = 12.

Answer.  x%5E4+%2B+4x%5E3+%2B+6x%5E2+%2B+4x+%2B+9 = 12 at x = sqrt%28-2%29-1.