Question

(x-5)^2=5x^2-(2x-1)(2x+1) решите уравнение с объяснением,пожалуйста

Answer 1

(x-5)²=5x²-(2x-1)(2x+1)
х²-10х+25=5х²-4х²+1
х²-5х²+4х²-10х=1-25
5х²-5х²-10х=-24
-10х=-24
х=-24:(-10)
х=2,4

Answer 2

Solving the Equation: (x-5)^2 = 5x^2 - (2x-1)(2x+1)

To solve the equation (x-5)^2 = 5x^2 - (2x-1)(2x+1), we can start by expanding and simplifying the equation.

Expanding the left side of the equation: (x-5)^2 = x^2 - 10x + 25

Expanding the right side of the equation: 5x^2 - (2x-1)(2x+1) = 5x^2 - (4x^2 - 1) = 5x^2 - 4x^2 + 1 = x^2 + 1

So, the equation becomes: x^2 - 10x + 25 = x^2 + 1

Subtracting x^2 from both sides: -10x + 25 = 1

Subtracting 25 from both sides: -10x = -24

Dividing by -10: x = 24/10 = 12/5

Therefore, the solution to the equation (x-5)^2 = 5x^2 - (2x-1)(2x+1) is x = 12/5.

Explanation

The solution to the equation is obtained by expanding and simplifying both sides of the equation and then solving for the variable x. The final solution is x = 12/5.