The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

Options

A. `14, 21`
B. `7,14`
C. `28,35`
D. `0,7`

Answer

A

Explanation

Let the required consecutive multiples of 7 be 7x and `7(x+1).`
Then, `(7x)^(2)+{7(x+1)]^(2)=637`
`implies" "49x^(2)+(7x+7)^(2)=637implies98x^(2)+98x-588=0`
`implies" "x^(2)-x-6=0impliesx^(2)+3x-2x-6=0`
`implies" "x(x+3)-2(x+3)=0implies(x+3)(x-2)=0`
`implies" "x+3=0" or "x-2=0`
`implies" "x=-3" or "x=2`
`implies" "x=2" "["neglecting "x=-3]`
Hence, the required numbers are `(7xx2)" and "(7xx3), i.e., 14` and 21.