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Usimov [2.4K]
3 years ago
7

For what values of a does the equation a+x= 1+xa^2 have no solution?

Mathematics
1 answer:
Anton [14]3 years ago
7 0

Answer:

We have the equation

a+x= 1+xa^2

we leave the terms with x on the left side of the equation and the independent terms on the right side.

x-xa^2=1-a\\(1-a^2)x=1-a\\

resolving for x we have that

x=\frac{1-a}{1-a^2}

Since we need that the equation doesn't have solution, then it is necessary that the denominator of x be 0 and this occur when 1-a^2=0\\1=a^2\\a=\pm1

Then, for a=\pm1 the equation hasn't solution

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