Question

(4x - 5)²=(x + 5)² как решить?

Answer 1

А так правильно??????????

Answer 2

To solve the equation (4x - 5)² = (x + 5)², we need to find the values of x that satisfy the equation. Let's go step-by-step to solve it:

Step 1: Expand both sides of the equation using the formula (a - b)² = a² - 2ab + b².

Expanding the left side: (4x - 5)² = (4x - 5)(4x - 5) = 16x² - 40x + 25

Expanding the right side: (x + 5)² = (x + 5)(x + 5) = x² + 10x + 25

Step 2: Now we have the equation: 16x² - 40x + 25 = x² + 10x + 25

Step 3: Move all the terms to one side of the equation by subtracting x², 10x, and 25 from both sides:

16x² - x² - 40x - 10x + 25 - 25 = 0

Step 4: Combine like terms:

15x² - 50x = 0

Step 5: Factor out the common term x from both terms:

x(15x - 50) = 0

Step 6: Set each factor to zero and solve for x:

a) x = 0 b) 15x - 50 = 0 15x = 50 x = 50/15 x = 10/3

So, the solutions to the equation (4x - 5)² = (x + 5)² are x = 0 and x = 10/3.