Mr. Beti was born in 1809 A. D. In the year x*x A. D. he was x-3years old. Find the value of X.
To find the value of X, we need to solve the equation:
1809 + X*X = (X - 3)
Let's solve it step by step:
Step 1: Expand the equation:
X * X = X - 3 - 1809
Step 2: Simplify:
X * X - X + 3 = -1809
Step 3: Move all terms to one side to form a quadratic equation:
X * X - X + 3 + 1809 = 0
Step 4: Simplify the equation further:
X * X - X + 1812 = 0
Now, we have a quadratic equation: X^2 - X + 1812 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. However, upon factoring, we get an irrational and complex root. Therefore, we will use the quadratic formula.
The quadratic formula states that for a quadratic equation in the form of ax^2 + bx + c = 0, the roots can be found using the formula:
X = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -1, and c = 1812.
Step 5: Substitute the values into the quadratic formula:
X = (-(-1) ± √((-1)^2 - 4 * 1 * 1812)) / (2 * 1)
X = (1 ± √(1 - 7248)) / 2
X = (1 ± √(-7247)) / 2
Since the square root of a negative number is not a real number, we conclude that there is no real value for X in this equation.