Question 190217
x^2+(x+7)^2=289
x^2+x^2+14x+49=289
2x^2+14x+49-289=0
2x^2+14x-240=0
2(x^2+7x-120)=0
2(x+15)(x-8)=0
x-8=0
x=8 ans. for the girl's age.
8+7=15 ans. for the boys age.
Proof:
8^2+15^2=289
64+225=289
289=289