Question

Find the two consecutive odd natural numbers such that the sum of their squares is 130

Answer 1

Let smaller odd no. be x
Therefore, larger odd no. = (x+2)
Sum of their squares = 130

=> x^2+(x+2)^2 = 130
=> x^2+x^2+4+4x = 130
=> 2x^2+4x+4-130 = 0
=> 2x^2+4x-126 = 0
=> x^2+2x-63 = 0 (dividing equation by 2)
=> x^2+9x-7x-63 = 0
=> x(x+9)-7(x+9) = 0
=> (x-7)(x+9) = 0
=> x = 7 or -9

Therefore, the consecutive odd numbers are:
=> 7 and 9
OR
=> -9 and -7

Answer 2

let one no. be x ..so other will be(x+2)..so..according to the question.. x^2+(x+2)^2=130...so..2x^2+4x+4=130=>x^2+2x+2=65....x^2+2x-63=0=>x^2+9x-7x-63=0=>(x+9)(x-7)=0=>x=-9 and x=7..so other no. will be..7+2=9..so no.s are 7 and 9 or -9 and -7