Question

find the roots of equation- ax 2 +a=a 2 x+x

Answer 1

Answer:

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Answer 2

Given,

$ax ^{2} + a \: = a ^{2}x + x$

To find,

The roots of the equation.

Solution,

The roots of the given equation will be a and 1/a.

We can easily solve this problem by following the given steps.

According to the question,

$ax ^{2} + a \: = a ^{2}x + x$

Moving (a²x+x) from the right-hand side to the left-hand side,

ax²-a²x-x+a = 0

Now, the root can be found by factorising it.

Taking ax common from the first two terms and -1 common

from the last terms,

ax(x-a) -1(x-a) = 0

Taking (x-a) common,

(x-a) (ax-1) = 0

(x-a) = 0, (ax-1) = 0

x = a, axe = 1

x = a, x = 1/a

Hence, the roots of the given equation is a and 1/a.