Question

(2x+3)(3x+1)+(5x+2)(2x+5)=(4x-1)^2 Решите уравнение ^-степень

Answer 1

1)6х^2+2х+9х+3+10х^2+25х+4х+10=16х^2-8х+1

2)16х^2+40х+13=16х^2-8х+1

3)40х+13=-8х+1

4)48х=-12

5)х=-0.25

(цифры со скобочками это номера строчек при решении)

Answer 2

To solve the equation, we need to simplify the left-hand side of the equation first and then solve for x. Let's start by expanding the expressions on the left-hand side:

(2x + 3)(3x + 1) + (5x + 2)(2x + 5) = (4x - 1)^2

Expanding the left-hand side:

(2x + 3)(3x + 1) + (5x + 2)(2x + 5) = 6x^2 + 2x + 9x + 3 + 10x^2 + 25x + 4x + 10 = 16x^2 + 31x + 13

Now we have the equation:

16x^2 + 31x + 13 = (4x - 1)^2

Now let's expand the right-hand side:

(4x - 1)^2 = (4x - 1)(4x - 1) = 16x^2 - 4x - 4x + 1 = 16x^2 - 8x + 1

So now the equation becomes:

16x^2 + 31x + 13 = 16x^2 - 8x + 1

To find the value of x, we need to move all the terms to one side of the equation:

16x^2 + 31x + 13 - 16x^2 + 8x - 1 = 0

Now simplify the equation:

31x + 12 = 0

To solve for x, isolate x on one side:

31x = -12

x = -12 / 31

The solution for x is approximately:

x ≈ -0.3871

Please note that this solution is an approximate value, rounded to four decimal places.