Chapter 10.4, Problem 28P

Solve each radical equation. Check your solution. If there is no solution, write no solution. $-f=\sqrt{-f+56}$

To determine

To find: the solution of the equation.

Answer to Problem 28P

There is no solution for equation.

Explanation of Solution

Given information:

The equation is $-f=\sqrt{-f+56}$ .

Calculation: to find the solution of the equation, first square and then simplify,

  $\begin{array}{l}-f=\sqrt{-f+56}\\ f^2=-f+56\text{ [square]}\\ f^2+f-56=0\text{ [simplify]}\\ \left(f+8\right)\left(f-7\right)=0\text{ [factorise]}\\ f=7,-8\end{array}$

Thus, there is no solution for equation because $f=7,-8$ does not lie in the domain of the equation.