Sumali sa IDNStudy.com at makakuha ng maraming kaalaman. Ang aming platform ng tanong at sagot ay idinisenyo upang magbigay ng mabilis at eksaktong sagot sa lahat ng iyong mga tanong.
Answer:
> Therefore, the brother is approximately 21.085 years old
> The girl is approximately 3.085 years old.
Explanation:
• Since the girl is 18 years younger than her brother, her age will be ( x - 18 ).
The problem states that the product of their ages is 65. This can be written as:
[tex]x(x - 18) = 65[/tex]
Now, let's solve this quadratic equation:
[tex]x^2 - 18x = 65[/tex]
[tex]x^2 - 18x - 65 = 0[/tex]
We can solve this using the quadratic formula, which is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]{( x^2 - 18x - 65 = 0 ), \text {the coefficients are:}}[/tex]
[tex] a = 1, \quad b = -18, \quad c = -65[/tex]
Plugging these into the quadratic formula:
[tex]x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot (-65)}}{2 \cdot 1}[/tex]
[tex]x = \frac{18 \pm \sqrt{324 + 260}}{2}[/tex]
[tex]x = \frac{18 \pm \sqrt{584}}{2}[/tex]
[tex]x = \frac{18 \pm 24.17}{2}[/tex]
This gives us two possible solutions:
[tex]x = \frac{18 + 24.17}{2} = \frac{42.17}{2} = \boxed {21.085}[/tex]
[tex] x = \frac{18 - 24.17}{2} = \frac{-6.17}{2} = \boxed {-3.085}[/tex]