Chapter 7: Q42. (page 462)

Solve the given equation.
$x^{2} (x + 2) = x (x^{2} + 2 x + 1)$

Short Answer

Expert verified

$x = 0$ is the solution of the given equation.

Step by step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $" = "$ .

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^{m} . a^{n} = a^{m + n}$

Where, $a$ is any non-zero real number.

Step 3. Solve the equation, x2(x+2)=x(x2+2x+1).

Use the power of a product rule to solve the equation.

$\begin{matrix} x^{2} (x + 2) = x (x^{2} + 2 x + 1) \\ x^{2} (x) + x^{2} (2) = x (x^{2}) + x (2 x) + x (1) \\ x^{3} + 2 x^{2} = x^{3} + 2 x^{2} + x \\ x^{3} + 2 x^{2} + x - x^{3} + 2 x^{2} = 0 \\ x = 0 \end{matrix}$

Therefore, $x = 0$ is the solution of the given equation.

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Equation	Related Expression	Power of ‘x’	Linear or non linear
$y = x$
$y = x^{2}$
$y = x^{3}$

Solve the given equation.
$x^{2} (x + 2) = x (x^{2} + 2 x + 1)$

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Define the power of a product rule.

Step 3. Solve the equation, x2(x+2)=x(x2+2x+1).

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Solve the given equation.x2(x+2)=x(x2+2x+1)

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Define the power of a product rule.

Step 3. Solve the equation, x2(x+2)=x(x2+2x+1).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the given equation.
$x^{2} (x + 2) = x (x^{2} + 2 x + 1)$