Question

find two consecutive odd integers, sum of whose square is 970.​

Answer 1

Answer:

Step-by-step explanation:

let the odd numbers be 2n+1 and 2n +3

(2n+1)^2 + (2n+3)^2 = 970

4n^2 + 1 + 4n + 4n^2 + 9  + 12n = 970

8n^2 + 16n = 970 - 10

n^2 + 2n = 120

n^2 + 2n - 120= 0

n^2 + 12n - 10n -120  = 0

n(n + 12 ) - 10 (n + 12 ) = 0

n = 10 or n = -12

n not equal to 12

thus n = 10

the odd integers are 21,23

therefore the numbers are