Question

Find three consecutive odd natural numbers the sum of whose squares is 155

Answer 1

let an odd natural no. = x
then, two odd natural no. just grater than x are x+2 and x+2+2=x+4

Acc. to ques:-

x^2 + (x+2)^2 + (x+4)^2= 155
x^2 + x^2 + 4 + 4x + x^2 +16 + 8x= 155
3x^2 + 12x + 20 = 155
3x^2 + 12x +20 - 155 = 0
3x^2 + 12x - 135 = 0
3(x^2 + 4x - 45) = 0
OR
x^2 + 4x - 45 = 0
x^2 + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x - 5) (x + 9) = 0

x-5=0                         OR                   x+9=0
x=5                                                     x=-9
-ve value will be rejected so x = 5
therefore 1st odd natural no. = 5
2nd odd natural no. = x + 2 => 5 + 2 = 7
3rd odd natural no. = x + 4 => 5 + 4=9

Answer=>  5, 7, 9

Answer 2

Plz tell by another method .