Application of Quadratic Equations.
A girl's age in 12 years' time is the square of her present age. Find her present age.
To find the girl's present age, let's assign a variable to represent her age.
Let's denote the girl's present age as "x".
According to the given information, her age in 12 years' time will be the square of her present age. So, her age in 12 years will be (x + 12).
The equation can be written as:
(x + 12) = x^2
Let's solve this equation step-by-step:
Step 1: Expand the equation
x + 12 = x^2
Step 2: Rearrange the equation in standard form
x^2 - x - 12 = 0
Step 3: Factorize the equation
(x - 4)(x + 3) = 0
Step 4: Set each factor equal to zero and solve for x
x - 4 = 0 => x = 4
x + 3 = 0 => x = -3
Since age cannot be negative, we can discard -3 as a solution.
Therefore, the girl's present age is 4 years old.
To solve this problem, we can use a quadratic equation.
Let's assume the girl's present age is represented by "x". According to the given condition, her age in 12 years' time will be the square of her present age, which means:
x + 12 = x^2
To solve this equation, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0. In our case, this gives us:
x^2 - x - 12 = 0
Now we can solve this quadratic equation to find the values of x. There are a few methods to solve quadratics, but one common approach is factoring. We need to find two numbers that multiply to give -12 and add up to -1. In this case, those numbers are -4 and 3:
(x - 4)(x + 3) = 0
Now we can set each factor equal to zero and solve for x:
x - 4 = 0 or x + 3 = 0
Solving these equations gives us two potential solutions:
x = 4 or x = -3
However, since we are talking about the girl's age, we can ignore the negative solution. Therefore, the present age of the girl is 4 years.
(x+12) = x^2
x^2 -x -12 = 0
(x-4)(x+3) = 0
x = 4 or -3
Sha can't have a negative age, so what does that leave you with?