Solving the Equation $x^2 + a^2 = (b - x)^2$ for x
We need to find the value of $x$ that satisfies the given algebraic equation.
Step-by-Step Solution
- Start with the given equation:
\(x^2 + a^2 = (b - x)^2\)
- Expand the term on the right side using the formula $(a - b)^2 = a^2 - 2ab + b^2$:
\(x^2 + a^2 = b^2 - 2bx + x^2\)
- Simplify the equation by subtracting $x^2$ from both sides:
\(a^2 = b^2 - 2bx\)
- Rearrange the equation to isolate the term containing $x$. Move $2bx$ to the left side and $a^2$ to the right side:
\(2bx = b^2 - a^2\)
- Solve for $x$ by dividing both sides by $2b$. Assume $b \neq 0$.
\(x = \frac{b^2 - a^2}{2b}\)
The value of $x$ satisfying the equation is $\frac{b^2 - a^2}{2b}$.
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
