Question

find two consecutive positive odd number,the sum of
whose square is 74

Answer 1

let one number be x then the other will be x+2 because they are odd numbers.
now according to the question the sum of their squares is 74
so, x^2 + (x+2)^2 = 74
solving them(see the image)
since the no. are positive therefore x=5 and the other no. is 7 .......(x+5)

Answer 2

let no. be x & x+2.
then, x^2 + (x+2)^2 =74
x^2 +x^2+4+2x=74
then,
2x^2 +2x+4-74=0
x^2+ 2x+2-37=0
x^2+2x-35=0
x^2+7x-5x-35=0
x(x+7)-5(x+7)=0
(x-5)(x+7)=0
x=5 & x=-7