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Question 22

The number of different integers $$x$$ that satisfy the equation $$\left(x^2-5x+5\right)^{\left(x^2-11x+30\right)}=1$$ is


Correct Answer: 6

Solution

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For a power to equal $$1$$, either the exponent is zero, the base is one, or the base is negative one with an even exponent. The exponent zero gives $$x=5,6$$, the base one gives $$x=1,4$$, and the base negative one gives $$x=2,3$$ with an even exponent. Thus there are $$6$$ distinct integer solutions.

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