Answer
$7,9$
Work Step by Step
Consecutive odd numbers have a difference between them of $2$. If we take the smaller odd number as $x$, the larger odd number is $(x+2)$. Since the sum of the squares of the two consecutive odd numbers is 130, we write the following equation and solve:
$x^{2}+(x+2)^{2}=130$
$x^{2}+x^{2}+4x+4=130$
$2x^{2}+4x+4-130=0$
$2x^{2}+4x-126=0$
$x^{2}+2x-63=0$
$x^{2}-7x+9x-63=0$
$x(x-7)+9(x-7)=0$
$(x-7)(x+9)=0$
$(x-7)=0$ or $(x+9)=0$
$x=7$ or $x=-9$
Disregarding the negative answer, we find that the smaller odd number is $7$. This means that the larger odd number is $7+2=9$.
