Solving the equation \(\displaystyle{\left({x}^{{2}}-{7}{x}+{11}\right)}^{{{\left({x}^{{2}}-{13}{x}+{42}\right)}}}={1}\). The question is to

Makayla Stevens

Makayla Stevens

Answered question

2022-04-02

Solving the equation (x27x+11)(x213x+42)=1.
The question is to find the number of positive integer values possible for x. The answer is 6. But I am only able to find 4(2,5,6,7). What are the other two possible values?

Answer & Explanation

zalutaloj9a0f

zalutaloj9a0f

Beginner2022-04-03Added 17 answers

I will give only the two other solutions the you missed. It is trick. Look carefully for the equation. RHS equal 1. if x213x+42 is even number. then x27x+11=1 is a solution. By factoring the last equation , we have x=3 and x=4. So, the set of solution is {2,3,4,5,6.7}
Cindy Reynolds

Cindy Reynolds

Beginner2022-04-04Added 7 answers

You forgot that (1)2n=1 for positive n. (The exponent is even). You have different cases for xy=1:
x=0,y=0
x=1,y=any real number
x=1,y=even number
You missed the last case.

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