Question

√5x-4 -x=0 через дискриминант

Answer 1

5x²-16-x²=0
4x²-16=0
2²x²-4²=0
2x-4=0
2x=4
x=2

Answer 2

To solve the equation √(5x - 4) - x = 0 using the discriminant, we first need to isolate the square root term on one side of the equation. Let's go step by step:

Step 1: Move the "x" term to the right side of the equation: √(5x - 4) = x

Step 2: Square both sides of the equation to eliminate the square root: (√(5x - 4))^2 = x^2

Step 3: Simplify the left side of the equation: 5x - 4 = x^2

Step 4: Rearrange the equation to standard quadratic form: x^2 - 5x + 4 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -5, and c = 4.

Step 5: Calculate the discriminant (Δ) of the quadratic equation using the formula Δ = b^2 - 4ac: Δ = (-5)^2 - 4 * 1 * 4 Δ = 25 - 16 Δ = 9

Step 6: Now, using the discriminant, we can find the solutions for the quadratic equation. The solutions are given by the quadratic formula: x = (-b ± √Δ) / 2a

Plugging in the values: x = (5 ± √9) / 2

Step 7: Simplify the square root: x = (5 ± 3) / 2

Now, we have two possible solutions:

1. x = (5 + 3) / 2 = 8 / 2 = 4
2. x = (5 - 3) / 2 = 2 / 2 = 1

So, the equation √(5x - 4) - x = 0 has two solutions: x = 4 and x = 1.