Radical Equations

Michigan State University - Diagnostic Exam

The solution set of the equation $√ ------ x + 1 + 1 = x$ is the same as the solution set for which of the following equations.

a) $x2 - 3x = 0$ b) $3x - 2 = 7$ c) $x = 0$

d) $2 x + 1 + 1 = x$ e) $x = 2$

Diagnostic:

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Solution:

√ ------ x + 1 + 1 = x √ ------ ⇒ x + 1 = x - 1 ( √------)2 2 ⇒ x + 1 = (x - 1) ⇒ x + 1 = x2 - 2x + 1 ⇒ 0 = x2 - 3x ⇒ 0 = x (x - 3 ) ⇒ x = 0, 3

Notice that only the solution, x = 3, satisfies the original equation. It follows that $√ ------ x + 1 + 1 = x$ is equivalent to $3x-2 = 7$

Diagnostic:

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July 15, 2008