Leah is 6 years older than her sister sarah. The product of their ages is 135. find their ages

Question

It is a hard question please answer it with solutions

Answer 1

x=Sarah's age

x+6=Leah's age

(x)(x+6)=135

x^2+6x=135

x^2+6x-135=0

135=3*3*3*5=(3*3)*(3*5)=9*15 and 15-9=6, the coefficient of the middle term

factor

(x+15)(x-9)=0

x-9=0

x=9 years old for Sarah

x+6=15 years old for Leah