The roots of the equation a(x^2 + 1) - (a^2 + | vedclass

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(A) Given equation: $a(x^2 + 1) - (a^2 + 1)x = 0$Expanding the terms: $ax^2 + a - a^2x - x = 0$Rearranging the terms: $ax^2 - a^2x - x + a = 0$Groupin

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$a, \frac{1}{a}$

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(A) Given equation: $a(x^2 + 1) - (a^2 + 1)x = 0$Expanding the terms: $ax^2 + a - a^2x - x = 0$Rearranging the terms: $ax^2 - a^2x - x + a = 0$Grouping the terms: $ax(x - a) - 1(x - a) = 0$Factoring out $(x - a)$: $(ax - 1)(x - a) = 0$Setting each factor to zero:$ax - 1 = 0 \implies x = \frac{1}{a}$$x - a = 0 \implies x = a$Therefore,the roots are $a$ and $\frac{1}{a}$.

The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

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