Q. 235 - Intermediate Algebra

Question

Simplify:

$\left(-4+\sqrt{17}\right)\left(-3+\sqrt{17}\right)$

Step-by-Step Solution

Answer

The value of the expression is $29-7\sqrt{17}$

Step 1. Given information

The given expression is $\left(-4+\sqrt{17}\right)\left(-3+\sqrt{17}\right)$

Step 2. Simplifying the expression

Multiplying the terms in the expression using distributive property we get:

$$\begin{gathered} \left(-4+\sqrt{17}\right)\left(-3+\sqrt{17}\right) \\ 12-4\sqrt{17}-3\sqrt{17}+{\left(\sqrt{17}\right)}^2 \end{gathered}$$

Adding or subtracting the like terms, we get:

$$\begin{gathered} -4\sqrt{17}-3\sqrt{17}+12+17 \\ -7\sqrt{17}+29 \\ 29-7\sqrt{17} \end{gathered}$$