Question

3. Чи є рівносильними рівняння. 1) х - 3 = 5 і 7x = 56; 3) x (во 2 степени)= -1 і |x| = -2 2) x+2=0 і х(х+2) = 0; Помогите пожалуйста

Answer 1

Відповідь:

Покрокове пояснення:

1) х-3=5

х=8

7х=56

х=8 рівносильні

3) $x^{2} =-1$ немає розв'язків

модуль х не може бути від'ємним немає розв'язків

2)х+2=0

х=-2

х(х+2)=0

х1=0

х2=-2

не є рівносильними

Answer 2

Are the equations of equal strength?

To determine if the equations are of equal strength, we need to solve each equation and compare the solutions.

1) x - 3 = 5 and 7x = 56: - Solving the first equation, we add 3 to both sides: x = 8. - Solving the second equation, we divide both sides by 7: x = 8. - The solutions for both equations are the same, so they are of equal strength.

2) x^2 = -1 and |x| = -2: - The equation x^2 = -1 has no real solutions because the square of any real number is always non-negative. - The equation |x| = -2 has no real solutions because the absolute value of any real number is always non-negative. - Both equations have no real solutions, so they are of equal strength.

3) x + 2 = 0 and x(x + 2) = 0: - Solving the first equation, we subtract 2 from both sides: x = -2. - Solving the second equation, we set each factor equal to zero: x = 0 or x + 2 = 0. - The solutions for the second equation are x = 0 and x = -2, which are the same as the solution for the first equation. - Therefore, the second equation is stronger because it has an additional solution.

In summary, the equations in the first and second examples are of equal strength, while the equation in the third example is stronger than the first equation.