given: The sum of the squares of two consecutive odd numbers is 394.
To find: the numbers.
Solution: Let the consecutive odd number be ‘a’ and a + 2
According to given condition,
a2 + (a + 2)2 = 394
Use the formula (x+y)2
= x2 + y2 + 2xy in (a + 2)2
Here x = a and y = 2,
⇒ a2 + a2 + 4 + 4a = 394
⇒ 2a2 + 4a +4 – 394 = 0
⇒ 2a2 + 4a – 390 = 0
Take 2 common out of the above equation,
⇒ a2 + 2a – 195 = 0
Factorise by splitting the middle term.
⇒ a2 + 15a – 13a – 195 = 0
⇒ a(a + 15) – 13(a + 15) = 0
⇒ (a – 13)(a + 15) = 0
Thus, a = 13, - 15
When a = 13 then a + 2 = 15
And when a = -15 then a + 2 = -13
So Consecutive odd numbers are 13, 15 and -15,-13.
