Question

23^2-(2x)^2=33^2-(3x)^2

Answer 1

Решение выглядит следующим образом :
529 - 4х^2 = 1089 - 9х^2
529 - 1089 = -9х^2 + 4х^2
-560 = -5х^2
х^2 = 112

Answer 2

To solve the equation, let's first simplify both sides and then solve for the value of "x".

Starting with the equation: 23^2 - (2x)^2 = 33^2 - (3x)^2

Step 1: Simplify the squares on both sides of the equation.

23^2 = 23 * 23 = 529 (2x)^2 = (2x) * (2x) = 4x^2

33^2 = 33 * 33 = 1089 (3x)^2 = (3x) * (3x) = 9x^2

Now, the equation becomes:

529 - 4x^2 = 1089 - 9x^2

Step 2: Move all the x^2 terms to one side of the equation.

To do this, let's add 9x^2 to both sides of the equation:

529 - 4x^2 + 9x^2 = 1089 - 9x^2 + 9x^2

Combine the x^2 terms:

529 + 5x^2 = 1089

Step 3: Move the constant term (529) to the other side of the equation.

To do this, let's subtract 529 from both sides:

529 + 5x^2 - 529 = 1089 - 529

Simplify:

5x^2 = 560

Step 4: Isolate "x" by dividing both sides by 5.

5x^2 / 5 = 560 / 5

x^2 = 112

Step 5: Solve for "x" by taking the square root of both sides.

√(x^2) = √112

x = ±√112

x ≈ ±10.583

So, the solutions for "x" are approximately x ≈ 10.583 and x ≈ -10.583.