Question

20. If x2 - x - 1 = 0, then the value of x3 - 2x + 1 is
(1) 0
(2) 2
1+ V5
1-15
(3)
(4)
2.
2
n
C​

Answer 1

Question :

If x² - x - 1 = 0, then the value of x³ - 2x + 1 is

Answer :

x³ - 2x + 1 = 2

Given :

x² - x - 1 = 0

To find :

x³ - 2x + 1 = ?

Step-by-step explanation :

       Given quadratic equation,

          x² - x - 1 = 0

It is of the form ax² + bx + c = 0

a = 1, b = -1, c = -1

where

    a  -  coefficient of x²

    b  -  coefficient of x

    c  -  constant term

We can solve it in two ways,

             ( I'm going to solve it in a simpler way )

1) by long method by finding the value of x and substituting it's value.

          $\boxed{\bf x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }$

2)  in a simpler way

     

      $\bf x^{2} -x-1=0 \\\\ => x^{2} -x=1\\\\=>x^{2} =x+1$

         $\bf {x^3-2x+1} \\\\ =x(x^2)-2x+1 \\\\ \it{substitute \ the \ value \ of \ x^2} \\\\ \bf =x(x+1)-2x+1 \\\\ =x^{2} +x-2x+1 \\\\ =x^{2} -x+1 \\\\ =1+1 \ \ \ [x^2-x=1]\\\\=2$

∴ x³ - 2x + 1 = 2