The sum of the squares of two consecutive odd numbers is `394.` Find the numbers.

Options

A. `12, 15`
B. `13, 15`
C. `14, 17`
D. `19, 17`

Answer

B

Explanation

Let the requaired consecutive odd numbers be x and `(x+2).` Then,
`x^(2)+(x+2)^(2)=394`
`implies" "2x^(2)+4x-390=0impliesx^(2)+2x-195=0`
`implies" "x^(2)+15x-13x-195=0`
`implies" "x(x+15)-13(x+15)=0`
`implies" "x+15=0" or "x-13=0`
`implies" "x=-15" or "x=13`
`implies" "x=13." "["rejecting "x=-15]`
Hence, the required numbers are `13` and `15.`