Question

(×+1)³-×(×+1)²+(×+1)

Answer 1

Answer:

$\boxed{x=-2}$ OR $\boxed{x=-1}$

Step-by-step-explanation:

NOTE :Kindly refer to the attachment first.

We have given that

$(x+1)^{3}-x\times(x+1)^{2}+(x+1)$

By using some identities, we can find the value of the given expression.

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

⟹ x³ + 3x² + 3x + 1 - x ( x² + 2x + 1 ) + ( x + 1 )=0

⟹ x³ + 3x² + 3x + 1 - x³ - 2x² - x + x + 1 = 0

⟹ 3x² + 3x + 1 - 2x² + 1 = 0

⟹ 3x² - 2x² + 3x + 1 + 1 = 0

⟹ x² + 3x + 2 = 0

⟹ x² + 2x + x + 2 = 0

⟹ x ( x + 2 ) + 1 ( x + 2 ) = 0

⟹ ( x + 2 ) ( x + 1 ) = 0

⟹ x + 2 = 0 OR x + 1 = 0

⟹ x = - 2 OR x = - 1

$\boxed{x=-2}$ OR $\boxed{x=-1}$

$\boxed{\begin{minipage}{7 cm} Fundamental Algebraic Identities \\ \\ \11)(a+b)^{2}=a^{2}+2ab+b^{2} \\ \\2)(a-b)^{2}=a^{2}-2ab+b^{2}\\ \\3)(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}\\ \\ \end{minipage}}$

Answer 2

Given :

• ( x + 1 )³ - x ( x + 1 )² + ( x + 1 )

To Find :

• Value of x

Solution :

➨ ( x + 1 )³ - x ( x + 1 )² + ( x + 1 )

➨ ( x³ + 3x² + 3x + 1 ) - x ( x² + 2x + 1 ) + ( x + 1 )

➨ x³ + 3x² + 3x + 1 - x³ - 2x² -x + x + 1

➨ x³ - x³ + 3x² - 2x² + 3x - x + x + 1 + 1

➨ x² + 3x + 2

By splitting middle term :

➨ x² + 2x + x + 2

➨ x ( x + 2 ) + 1 ( x + 2 )

➨ ( x + 1 ) ( x + 2 )

To Find value of x let this equation = 0

➨ ( x + 1 ) ( x + 2 ) = 0

➨ x + 1 = 0

➨ x = - 1

➨ x + 2 = 0

➨ x = -2

Identities used :

➨ ( a + b )³ = a³ + 3a²b + 3ab² + b³

➨ ( a + b )² = a² + 2ab + b²