X-√x+1=5

Question 1

Задача Задача №56861

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Аноним

24 ноября 2023 03:58 · публичный вопрос

А

Аноним 24 ноября 2023 03:58

X-√x+1=5

Answer

To solve the equation x - √(x + 1) = 5, we can follow these steps:

Start by isolating the square root term on one side of the equation: x - 5 = √(x + 1)
Square both sides of the equation to eliminate the square root: (x - 5)^2 = (√(x + 1))^2 x^2 - 10x + 25 = x + 1
Simplify the equation: x^2 - 10x + 25 - x - 1 = 0 x^2 - 11x + 24 = 0
Factor the quadratic equation: (x - 3)(x - 8) = 0
Set each factor equal to zero and solve for x: x - 3 = 0 OR x - 8 = 0 x = 3 OR x = 8

So the two possible solutions for the equation x - √(x + 1) = 5 are x = 3 and x = 8.

Question 2

x-√x+1=5

Answer

To solve the equation x - √(x + 1) = 5, we can follow these steps: 1. Start by isolating the square root term on one side of the equation: x - 5 = √(x + 1) 2. Square both sides of the equation to eliminate the square root: (x - 5)^2 = (√(x + 1))^2 x^2 - 10x + 25 = x + 1 3. Simplify the equation: x^2 - 10x + 25 - x - 1 = 0 x^2 - 11x + 24 = 0 4. Factor the quadratic equation: (x - 3)(x - 8) = 0 5. Set each factor equal to zero and solve for x: x - 3 = 0 OR x - 8 = 0 x = 3 OR x = 8 So the two possible solutions for the equation x - √(x + 1) = 5 are x = 3 and x = 8.