Chapter 8.2, Problem 48HP

To determine

To state: If there is any value of x for which the statement ${\left(x+2\right)}^2=x^2+2^2$ is true? If so, fond a value of x . Explain your reasoning.

Answer to Problem 48HP

The given statement is true for $x=0$

Explanation of Solution

Given:

  ${\left(x+2\right)}^2=x^2+2^2$

Calculation:

The given equation is ${\left(x+2\right)}^2=x^2+2^2$

Simplify the left hand side of the equation using the formula ${\left(a+b\right)}^2=a^2+2ab+b^2$

  $x^2+2\cdot 2\cdot x+2^2=x^2+2^2$

Now, in order to both sides of equation equal,

  $\begin{array}{c}2\cdot 2\cdot x=0\\ 4x=0\\ x=0\end{array}$

So, for $x=0$ , the given statement is true.