What extraneous solution arises when the question √(x+3)=2x is solved for x by f

Mathematics
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What extraneous solution arises when the question √(x+3)=2x is solved for x by first squaring both sides of the equation?

May 12th, 2015

When we square both sides we get:  x + 3 = 4x^2

To solve, we need it equal to zero:  4x^2 - x - 3 = 0

Factoring we get: (4x + 3)(x - 1) = 0

This gives us x = -3/4   and  x = 1

The x = 1 is a fine answer when we plug it back in.  However, the -3/4 doesn't work.  It is therefore, extranious.

Hope that helps.

May 12th, 2015

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May 12th, 2015
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