Question

solve:: x³-3x²+3x-1=0 ​

Answer 1

Step-by-step explanation:

x³ - 3x² + 3x - 1 = 0

x³ - 1 - 3x² + 3x = 0

(x-1)(x²+x+1) -3x(x-1) = 0

(x-1) (x²+x+1-3x) = 0

(x-1) (x²-2x+1) = 0

(x-1) (x-1)² = 0

(x-1)³ = 0

x = 1 , 1 , 1

Answer 2

TOPIC :- FACTORISING THE CUBIC EQUATION

CONCEPT USED :- First , by hit and trial method, find any root any then divide the cubic equation by the factor you have got to get another zeroes

x³ - 3x² + 3x - 1 = 0.

By hit and trial method, we observe that (1) is a zero of the equation.Hence, x - 1 is one of the factor.

x³ - 3x² + 3x - 1

= x³ - x² - 2x² + 2x + x - 1

= x²(x - 1) -2x ( x-1) +1(x-1)

= (x² - 2x +1) (x-1)

=(x-1)² (x - 1)

= (x - 1)³

Hence, the roots of the equation are equal and is 1.

Regards

Kshitij