Question -
Answer -
Let two consecutive positive integers be x and x + 2
A.T.Q.,
(x)2 + (x + 2)2 = 970
=> x2 + x2 + 4x + 4 – 970 = 0
=> 2x2 + 4x – 966 = 0
=> x2 + 2x – 483 = 0 (Dividing by 2)
=> x2 + 23x – 21x – 483 = 0
=> x (x + 23) – 21 (x + 23) = 0
=> (x – 21) (x + 23) = 0
Either x – 21 = 0 or x + 23 = 0
x = 21 or x = – 23 (rejected being -ve)
As integers should be +Ve
x = 21 and x + 2 = 21 + 2 = 23
Hence integers are 21, 23