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Question 55
How many disticnt positive integer-valued solutions exist to the equation $$(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$$ ?
Solution
$$(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$$
if $$(x^{2}-13x+42)$$=0 or $$(x^{2}-7x+11)$$=1 or $$(x^{2}-7x+11)$$=-1 and $$(x^{2}-13x+42)$$ is even number
For x=6,7 the value $$(x^{2}-13x+42)$$=0
$$(x^{2}-7x+11)$$=1 for x=5,2.
$$(x^{2}-7x+11)$$=-1 for x=3,4 and for X=3 or 4, $$(x^{2}-13x+42)$$ is even number.
.'. {2,3,4,5,6,7} is the solution set of x.
.'. x can take six values.
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