Question

Рівняння: 5x²-8x+3=0 Поможіть будь ласка..

Answer 1

Відповідь :Х1= 3/5; Х2= 1.

Answer 2

Solving the Equation: 5x² - 8x + 3 = 0

To solve the equation 5x² - 8x + 3 = 0, we can use the quadratic formula or factorization method. Let's go through both methods.

Method 1: Quadratic Formula

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0, where a, b, and c are constants.

For the equation 5x² - 8x + 3 = 0, we have: a = 5, b = -8, and c = 3.

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values of a, b, and c into the formula, we get: x = (-(-8) ± √((-8)² - 4(5)(3))) / (2(5)).

Simplifying further: x = (8 ± √(64 - 60)) / 10.

x = (8 ± √4) / 10.

Now, we have two possible solutions: x₁ = (8 + 2) / 10 = 10 / 10 = 1. x₂ = (8 - 2) / 10 = 6 / 10 = 0.6.

Therefore, the solutions to the equation 5x² - 8x + 3 = 0 are x = 1 and x = 0.6.

Method 2: Factorization

To solve the equation 5x² - 8x + 3 = 0 using factorization, we need to find two numbers whose product is equal to the product of the coefficient of x² (5) and the constant term (3), and whose sum is equal to the coefficient of x (-8).

The factors of 5 are 1 and 5, and the factors of 3 are 1 and 3. We need to find two numbers that satisfy the conditions mentioned above.

By trial and error, we find that the factors 1 and 3 satisfy the conditions. Therefore, we can rewrite the equation as follows: 5x² - 3x - 5x + 3 = 0.

Now, we can factor by grouping: x(5x - 3) - 1(5x - 3) = 0.

Notice that we have a common factor of (5x - 3). Factoring it out, we get: (5x - 3)(x - 1) = 0.

Setting each factor equal to zero, we have: 5x - 3 = 0, which gives x = 3/5. x - 1 = 0, which gives x = 1.

Therefore, the solutions to the equation 5x² - 8x + 3 = 0 are x = 3/5 and x = 1.

Please let me know if you need any further assistance!