Question

If X=1/2-√3,find the value of x^3-2x^2-7x+5
(Express x^3-2x^2-7x+5 in terms of x^2-4x+1)

Answer 1

Step-by-step explanation:

x = 1/2-√3

by rationalizing

x = 1/2-√3 * 2+√3/2+√3

x = 2+√3/2² - √3²

x = 2+√3/4-3

x= 2+√3

squaring both sides...

x² =(2+√3)²

x² = 4 + 3 + 2*2*√3

x² = 7 +4√3

now equating...

x³-2x²-7x+5

x³ - 7x -2x² +5

x(x² - 7) - 2x² +5

x( 7+4√3 -7) - 2(7+4√3) +5

2+√3 ( 4√3) - 14 - 8√3 +5

4√3 * 2 + √3* 4√3 - 9 -8√3

8√3 +12 -9-8√3

12 -9 = 3.... is the answer...

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