Question

A positive number is 5 larger than another positive number, the sum of the squares of the two positive number is 53. Find the numbers. Show how you found the solutions

Answer 1

Let:

x = 1st unknown number

y = 2nd unknown number

A positive number is 5 larger than another positive number:

`x=5y_{\text{ }}(1)`

the sum of the squares of the two positive number is 53:

`x^2+y^2=53_{\text{ }}(2)`

Replace (1) into (2):

`\begin{gathered} (5y)^2+y^2=53 \\ 25y^2+y^2=53 \\ 26y^2=53 \\ y^2=(53)/(26) \\ y=\pm\sqrt[]{(53)/(26)} \\ \end{gathered}`

Replace y into (1):

`x=\pm5\sqrt[]{(53)/(26)}`

Since the numbers are positive:

`\begin{gathered} x=5\sqrt[]{(53)/(26)} \\ y=\sqrt[]{(53)/(26)} \end{gathered}`