Q 6.94 - Intermediate Algebra

Question

Solve, $(k+1)(k-1)=8$

Step-by-Step Solution

Answer

The value is $k=\pm 3$

Step 1: Given information

Given the equation, $(k+1)(k-1)=8$

Step 2: Multiply the binomials

Multiplying the binomials, we get

$$\begin{gathered} (k+1)(k-1)=8 \\ {k}^2-1=8 \\ {k}^2=9 \\ k=\pm 3 \end{gathered}$$

Step 3: Checking the value

Substituting and checking, we get

$$\begin{gathered} (k+1)(k-1)=8 \\ (3+1)(3-1)=8 \\ 4\times 2=8 \\ 8=8 \\ (-3+1)(-3-1)=8 \\ -2\times -4=-8 \\ 8=8 \end{gathered}$$

So the value is correct