Answer:
(a) \((x-7)(x+7)=95\)
(b) Trina is 12 years old.
Step-by-step explanation:
(a)
Let x represents trinas age.
It is given that trina has two brothers. one brother is 7 years older than trina and the other brother is 7 years younger than trina.
Age of elder brother = x+7 years
Age of youger brother = x-7 years
Product of her brothers age = \((x-7)(x+7)\)
It is given that the product of her brothers age is 95.
\((x-7)(x+7)=95\)
(b)
We need to solve the equation
\((x-7)(x+7)=95\)
\(x^2-7^2=95\) \([\because a^2-b^2=(a-b)(a+b)]\)
\(x^2-49=95\)
Add 49 on both sides.
\(x^2=95+49\)
\(x^2=144\)
Taking square root both sides.
\(x=\pm \sqrt{144}\)
\(x=\pm 12\)
The values of x are -12 and 12. But age of a person can not be negative.
Therefore value of x is 12. It means trina is 12 years old.
