Question

if x is equals to 1 upon 2 minus root 3 find the value of x cube minus 2 x square - 7 x + 5

Answer 1

Answer:

value of x³ - 2x² -7x + 5  is 3.

Step-by-step explanation:

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

To find: Value of x³ - 2x² -7x + 5

First we simplify the x,

$x=\frac{1}{2-\sqrt{3}}=\frac{1}{2-\sqrt{3}}\times\frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2+\sqrt{3}}{4-3}=2+\sqrt{3}$

Now, we find x²,

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

 $=\frac{1}{4+3-4\sqrt{3}}=\frac{1}{7-4\sqrt{3}}\times\frac{7+4\sqrt{3}}{7+4\sqrt{3}}$

 $=\frac{7+4\sqrt{3}}{49-48}=7+4\sqrt{3}$

Now, we find x³,

$x^3=x^2\times x=(2+\sqrt{3})\times(7+4\sqrt{3})=14+8\sqrt{3}+7\sqrt{3}+12=26+15\sqrt{3}$

Now,

x³ - 2x² -7x + 5

= ( 26 + 15√3 ) - 2( 7 + 4√3 ) - 7( 2 + √3 ) + 5

= 26 + 15√3 - 14 - 8√3 - 14 - 7√3 + 5

= 26 + 15√3 - 14 - 8√3 - 14 - 7√3 + 5

= 3

Therefore, value of x³ - 2x² -7x + 5  is 3

Answer 2

Answer:

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