16 / x = x^2 / 4

Answer:

4

Explanation:

Welcome, math enthusiasts! This challenge is a classic algebraic riddle that tests your equation-solving skills. Don’t let the ‘x’ intimidate you; with a few fundamental steps, we’ll uncover its true value together!

To crack this equation, we need to isolate ‘x’. Let’s break it down step by step:

• The Equation: We start with the given equation: 16 / x = x² / 4
• Step 1: Cross-Multiplication: To eliminate the denominators and simplify, we’ll cross-multiply both sides of the equation. This means multiplying the numerator of the first fraction by the denominator of the second, and vice-versa.
  • (16) * (4) = (x) * (x²)
• Step 2: Simplify Both Sides: Now, perform the multiplication on each side:
  • 64 = x³
• Step 3: Isolate x (Cube Root): To find ‘x’, we need to undo the operation of ‘cubing’ it. The inverse of cubing is taking the cube root. We’ll take the cube root of both sides of the equation:
  • ³√64 = ³√x³
• Step 4: Final Calculation: The cube root of 64 is the number that, when multiplied by itself three times, equals 64.
  • 4 * 4 * 4 = 64

So, applying these steps, the value of x that satisfies the equation 16 / x = x² / 4 is: 4

Did you solve it correctly? Great job if you did! This equation-solving brain teaser is a fantastic way to sharpen your algebraic thinking. Share this math puzzle with friends and family and see who can solve for x the fastest!