Question

Уравнение: 1)5x²–3x+1=0 2)3x²–3=0.

Answer 1

Відповідь:

Пояснення:

    1)  5x²–3x + 1 = 0 ;

       D = (- 3 )² - 4*5*1 = 9 - 20 = - 11 < 0 ;   xЄ ∅ ; ( немає коренів )

   2) 3x²–3 = 0 ;

       3х² = 3 ;

         х² = 1 ;

         х₁,₂ = ± √1 ;     х₁,₂ = ± 1 . (два корені )

Answer 2

1. To solve the equation 5x² - 3x + 1 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 5, b = -3, and c = 1. Plugging these values into the quadratic formula, we have:

x = (-(-3) ± √((-3)² - 4 * 5 * 1)) / (2 * 5) = (3 ± √(9 - 20)) / 10 = (3 ± √(-11)) / 10

Since the discriminant (b² - 4ac) is negative (-11), the solutions will be complex numbers.

Therefore, the solutions to the equation 5x² - 3x + 1 = 0 are: x = (3 + √(-11)) / 10 x = (3 - √(-11)) / 10

2. To solve the equation 3x² - 3 = 0, we can factor it or use the quadratic formula. Let's use the quadratic formula here as well.

For this equation, a = 3, b = 0, and c = -3. Plugging these values into the quadratic formula, we have:

x = (-0 ± √(0² - 4 * 3 * (-3))) / (2 * 3) = (0 ± √(0 + 36)) / 6 = (0 ± √36) / 6 = (0 ± 6) / 6

Simplifying further, we get:

x = 6 / 6 = 1 x = -6 / 6 = -1

Therefore, the solutions to the equation 3x² - 3 = 0 are: x = 1 x = -1