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For 1 ≤ $x$ ≤ 2, simplify √ $(x + 2$ √ $(x - 1)$ ) + √ $(x - 2$ √ $(x - 1)$ ).

Competition practiceAlgebra

A2
B2√ $(x - 1)$
C2√ $x$
D $x$

Step-by-Step Solution

x

± 2√

(x - 1)

= (√

(x - 1)

± 1)². For 1 ≤

x

≤ 2, √

(x - 1)

≤ 1, so the sum is (√

(x - 1) + 1

) + (1 − √

(x - 1)

) = 2.

Answer: A) 2

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