Question

Решить уравнения. 1. 4x+x²+1=x(2+x) 2. 3x(x+1)-2x(5x+3)=7x(2-x)+34Решите пожалуйста!!​

Answer 1

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Answer 2

To solve the given equations, let's go through each one step by step:

1. Equation 1: 4x + x² + 1 = x(2 + x) + 2

To solve this equation, we need to simplify both sides and then solve for x.

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

Now, let's rewrite the equation: 4x + x² + 1 = 2x + x² + 2

Combining like terms: 4x - 2x + x² - x² + 1 - 2 = 0

Simplifying further: 2x - 1 = 0

To isolate x, we can add 1 to both sides: 2x = 1

Finally, divide both sides by 2: x = 1/2

Therefore, the solution to Equation 1 is x = 1/2.

2. Equation 2: 3x(x + 1) - 2x(5x + 3) = 7x(2 - x) + 34

To solve this equation, we'll follow a similar process of simplifying and solving for x.

Expanding the left side: 3x(x + 1) - 2x(5x + 3) = 3x² + 3x - 10x² - 6x

Expanding the right side: 7x(2 - x) + 34 = 14x - 7x² + 34

Now, let's rewrite the equation: 3x² + 3x - 10x² - 6x = 14x - 7x² + 34

Combining like terms: 3x - 6x + 3x² - 10x² - 14x + 7x² = 34

Simplifying further: -17x² - 17x + 34 = 0

Dividing the entire equation by -17 to simplify: x² + x - 2 = 0

Now, we can factor the quadratic equation: (x + 2)(x - 1) = 0

Setting each factor equal to zero: x + 2 = 0 or x - 1 = 0

Solving for x in each case: x = -2 or x = 1

Therefore, the solutions to Equation 2 are x = -2 and x = 1.

In summary, the solutions to the given equations are: - Equation 1: x = 1/2 - Equation 2: x = -2, x = 1