Question

The sum of square of two consecutive odd numbers is 514.find those numbers

Answer 1

Let the two consecutive no. be x &x+2
A.T.Q
x^2+(x+2)^2=514
x^2+x^2+4+4x=514
2x^2+4x=514-4
2x^2+4x=510
2x^2+4x-510
x^2+2x-255
x^2+17x-15x-255
x(x+17)-15(x+17)
(x+17)(x-15)
x+17=0
x=-17
&
x-15=0
x=15
if the odd no. is
x=-17
X+2=-17+2
x=-15......
if the odd no. is
x=15
x+2..
x=15+2
x=17
those no. can be -17 or-15
or it can be 15 or 17
hope it helps you......
thanks...

Answer 2

Solutions :-

Given : Sum of squares = 514
Let one of the odd positive integer be x 
So, other odd positive integer is x+2

Now,
The sum of squares = x² +(x+2)²
= x² + x² + 4x +4
 = 2x² + 4x + 4

⇒ 2x² +4x + 4 = 514
⇒ 2x² +4x = 514 - 4 = 510
⇒ 2x² + 4x - 510 = 0 
⇒ 2(x² + 2x - 255) = 0 
⇒ x² + 2x - 255 = 0
⇒ x² + 17x - 15x -143 = 0 
⇒ x (x+17) - 15 (x+17) = 0 
⇒ (x + 17) (x - 15) = 0
⇒ x = 15 or -17
We always take positive value of x


Answer :
one of the odd positive integer = x = 15
other odd positive integer = x + 2 = 15 + 2 = 17