Question

please solve it and find the value of X

Answer 1

Given Equation is x^3 - 6x^2 + 11x - 6 = 0

= > x^3 - x^2 - 5x^2 + 5x + 6x - 6 = 0

= > x^2(x - 1) - 5x(x - 1) + 6(x - 1) = 0

= > (x^2 - 5x + 6)(x - 1) = 0

= > (x^2 - 3x - 2x + 6)(x - 1) = 0

= > (x(x - 3) - 2(x - 3))(x - 1) = 0

= > (x - 2)(x - 3)(x - 1) = 0

= > x = 1,2,3.

Hope this helps!

Answer 2

Equation : x³ - 6x² + 11x - 6 = 0


x³ - 6x² + ( 5 + 6 ) x - 6 = 0

=> x³ - 6x² + 5x + 6x - 6 = 0


=> x³ - ( 1 + 5 )x² + 5x + 6x - 6 = 0


=> x³ - x² - 5x² + 5x + 6x - 6 = 0


=> x²( x - 1 ) - 5x( x - 1 ) + 6( x - 1 ) = 0


=> ( x - 1 ) ( x² - 5x + 6 ) = 0

=> ( x - 1 ) ( x² - 2x - 3x + 6 ) = 0


=> ( x - 1 ) [ x( x - 2 ) - 3( x - 2 )] =0


=> ( x - 1 ) ( x - 2 ) ( x - 3 ) = 0


Hence,

x - 1 = 0
=> x = 1

x - 2 = 0
=> x = 2

x - 3 = 0
=> x = 3
$.$


x = 1 or 2 or 3