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:

$\huge{\purple{\underline{\underline{\mathcal{Answer}}}}}$

$x = \frac{1}{2 - \sqrt{3} }$

now.. by rationalizing...

$x = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$x = \frac{2 + \sqrt{3} }{ {2}^{2} - \sqrt{3 ^{2} } }$

${\boxed{x = 2+{\sqrt3}}}$

squaring both sides..

x² =(2+√3)²

x² = 4 + 3 + 2*2*√3

${\boxed{\squarex= 7+4{\sqrt3}}}}}$

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...

thank you

hope it helps ❤️❤️

plz mark it as brainliest