Question

if x = 1/2-root3 then find the x³ - 2x² - 7x + 5​

Answer 1

$\bold{Answer}$



$\bold {Step by Step Solution}$

${x}^{3} - 2 {x}^{2} - 7x + 5$

=>

$= {x}^{3} - 7x - 2 {x}^{2} + 5$

$= x( {x}^{2} - 7) - 2 {x}^{2} + 5$

.

Now,

put

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


by rationalisation

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

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

$= 2 + \sqrt{3}$

value of X then we get,

${x}^{2} = {(2 + \sqrt{3}) }^{2}$

$= 4 + 3 + 4 \sqrt{3}$

$= 7 + 4 \sqrt{3}$



$\bold{By using above eq }$

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

$= (2 - \sqrt{3} )(7 + 4 \sqrt{3} - 7 ) - 2(7 + 4 \sqrt{3} ) + 5$

$= 8 \sqrt{3} + 12 - 14 - 8 \sqrt{3} + 5$

$- 2 + 5$

$= 3$

Answer 2

Answer:

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