Answer
k = 10
Step-by-step explanation
[tex]\begin{gathered} \text{The square of k is 69 less than the square of k+ 3} \\ is\text{ means equal to in mathematics} \\ \text{Mathematically, we have the following equation} \\ k^2=(k+3)^2\text{ - 69} \\ \text{open the parenthesis} \\ k^2=k^2\text{ + 6k + 9 - 69} \\ k^2=k^2\text{ + 6k - 60} \\ \text{Collect the like terms} \\ k^2-k^2\text{ = 6k - 60} \\ 0\text{ = 6k - 60} \\ -6k\text{ = -6}0 \\ \text{Divide through by - 6} \\ \frac{-6k}{-6}\text{ = }\frac{-60}{-6} \\ k\text{ = 10} \end{gathered}[/tex]Hence, k = 10
