Chapter 9.3, Problem 2E

To determine

To explain which is different.

Answer to Problem 2E

  $x^2+146=2$ is different

Explanation of Solution

Given information:

Solve $x^2=144$ using square roots

Solve $x^2-144=0$ using square roots

Solve $x^2+146=2$ using square roots

Solve $x^2+2=146$ using square roots

Calculation:

Solve $x^2=144$ using square roots

  $x^2=144$

On solving

  $x=\sqrt{144}$

On solving

  $x=12,-12$

Solve $x^2-144=0$ using square roots

  $x^2-144=0$

On solving

  $x^2=144$

On solving

  $x=\sqrt{144}$

On solving

  $x=12,-12$

Solve $x^2+146=2$ using square roots

  $x^2+146=2$

On solving

  $x^2=-144$

On solving

  $x=\sqrt{-144}$

On solving

  $x=12i$

Solve $x^2+2=146$ using square roots

  $x^2+2=146$

On solving

  $x^2=144$

On solving

  $x=\sqrt{144}$

On solving

  $x=12,-12$

Hence, $x^2+146=2$ is different