SOLUTION: solve : (x² + 3x +1)^(x² +7x +12) = 1

Question 1148967: solve : (x² + 3x +1)^(x² +7x +12) = 1
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The equation is satisfied if...

(1) (x^2+7x+12) = 0 (any number to the 0 power is 1)

(2) (x^2 +3x+1) = 1 (1 raised to any power is 1)

(3) (x^2+3x+1) = -1 AND (x^2+7x+12) is even (-1 raised to an even power is 1)

(1)
x = -3 and x = -4 are solutions.

(2)

x = -3 and x = 0 are solutions (x = -3 is already known to be a solution).

(3)

x = -1 and x = -2 are solutions IF they make x^2+7x+12 = (x+3)(x+4) even.

Note that, for both x = -1 and x = -2, (x+3)(x+4) are consecutive integers. One of them has to be even and one odd; so their product is even. Therefore, both x = -1 and x = -2 are solutions.

ANSWER: The solutions are 0, -1 -2, -3, and -4.

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