Alternating signs
⎩ ⎪ ⎨ ⎪ ⎧ x 2 x 3 x 4 = = = 1 − 1 1
If all the equations above are true. Then what is the value of x ?
The answer is -1.
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2 solutions
It should be − 1 .
How do you know that the answer must be -1? Maybe there's another value that also satisfy these conditions?
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would you mind defining your question by logic?
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You have shown that a solution to (x) is -1, but is that the only solution?
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@Pi Han Goh – i think for these equation -1 is the only answer. do you know another?
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@Mohammad Khaza – As a solution writer, you are supposed to explain why x=-1 is the only solution, not me.
The only value of x that satisfies x 3 = − 1 is x = − 1 . Because we are given that all of the equations are true, however, we must check that − 1 satisfies all of the other equations.
( − 1 ) 2 = 1
( − 1 ) 4 = 1
Sure enough it does. Thus, x = − 1 .
( − 1 ) 2 =1
( − 1 ) 3 =-1
( − 1 ) 4 =1
it's clearly -1