Question

One positive number is 5 more than another. The sum of their squares is 53. What is the larger number?

Answer 1

7

1) Let's write this

1st number: x

2nd number: y+5

So the positive number and the 1st number have the following relationship x = y +5

2) So we can write, and expand that binomial:

y² +(y+5)² = 53

y² + y² +10y +25 = 53 Combine like terms

2y² +10y -28 =0

We can now solve it:

`\begin{gathered} y=\frac{-10\pm\sqrt[]{100-4(2)(-28)}}{2(2)} \\ y_1=2 \\ y_2=-7 \end{gathered}`

3) As -7 is 9 units lower than 2, then it does not suits us. So let's use that prior relationship to find the other number

x =y+5

x = 2 +5

x=7

Hence, the larger number is 7 and the smaller one is 2