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Let $x = 1$ /(2 − √3). Find the value of $x^{3} - 2 x^{2} - 7 x + 5$ .

Competition practiceAlgebra

A3
B5
C1
D2√3

Step-by-Step Solution

x = 2

+ √3, so

(x - 2)^{2} = 3

, i.e.

x^{2} - 4 x + 1 = 0

. Dividing,

x^{3} - 2 x^{2} - 7 x + 5 = (x + 2) (x^{2} - 4 x + 1) + 3 = 3

.

Answer: A) 3

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