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Question
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
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Solution
We have been given
a(x2 + 1) - x(a2 + 1) = 0
ax2 - (a2 + 1)x + a = 0
ax2 - a2x - x + a = 0
ax(x - a) - 1(x - a) = 0
(ax - 1)(x - a) = 0
Therefore,
ax - 1 = 0
ax = 1
x = 1/a
or,
x - a = 0
x = a
Hence, x = 1/a or x = a
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