Question

Solve the equation $\frac{15}{p}+p=16$. Check your solution.

Short answer

The solution for the equation is $p=1,15$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $\frac{15}{p}+p=16$.

Step 2. Simplify the equation.

The given equation $\frac{15}{p}+p=16$is solved as:

$\begin{array}{l}\frac{15}{p}+p=\mathrm{16....}\left(\text{Given}\right)\\ 15+p^2=16p\\ p^2-16p+15=0\\ \left(p-15\right)\left(p-1\right)=0\\ p=1,15\end{array}$

Step 3. Verify the result for obtained value.

Plugging $p=1,15$in given equation and verify the result.

$\begin{array}{l}\frac{15}{p}+p=\mathrm{16....}\left(\text{Given}\right)\\ \frac{15}{\left(1\right)}+\left(1\right)=\mathrm{16....}\left(\text{For}p=1\right)\\ 16=\mathrm{16....}\left(\text{Truefor}p=1\right)\\ \frac{15}{p}+p=\mathrm{16....}\left(\text{Given}\right)\\ \frac{15}{\left(15\right)}+\left(15\right)=\mathrm{16....}\left(\text{For}p=15\right)\\ 16=\mathrm{16....}\left(\text{Truefor}p=15\right)\end{array}$

Hence the solution is verified for $p=1,15$.

Step 4. Conclusion.

The solution for the given equation is $p=1,15$.