Question

Solve the following radical equation. Enter your answer as an integer. If there is no solution indicate "No Solution" sqrt(5t - 11) = t - 1

Answer 1

ANSWER

`t=4,3`

Step-by-step explanation

Given;

`√(5t-11)=t-1`

Square both sides;

`\begin{gathered} \left(√(5t-11)\right)^2=\left(t-1\right)^2 \\ 5t-11=t^2-2t+1 \end{gathered}`

Solve and switch the sides;

`\begin{gathered} 5t-11=t^2-2t+1 \\ t^2-2t+1=5t-11 \end{gathered}`

Add 11 to both sides and simplify;

`\begin{gathered} t^2-2t+1+11=5t-11+11 \\ t^2-2t+12=5t \end{gathered}`

subtract 5t from both sides

`\begin{gathered} t^2-2t+12-5t=5t-5t \\ t^2-7t+12=0 \end{gathered}`

Solve the quadratic equation;

`\begin{gathered} t_(1,\:2)=(-\left(-7\right)\pm √(\left(-7\right)^2-4\cdot \:1\cdot \:12))/(2\cdot \:1) \\ t_1=(-\left(-7\right)+1)/(2\cdot \:1) \\ t_2=(-\left(-7\right)-1)/(2\cdot \:1) \\ t_1=(8)/(2)=4\frac{}{} \\ t_2=(6)/(2)=3 \\ \end{gathered}`

Therefore the solution to the quadratic equation are t=4, t=3