Question

1)√(x-7)+√(17-x)=42)3√(x²-4)+1=3x+7решите пожалуйстазаранее спасибо

Answer 1

1)\$\sqrt{x-7}+\sqrt{17-x}=4\\ \sqrt{x-7}=4-\sqrt{17-x}\\ x-7=16-8\sqrt{17-x}+17-x\\ 8\sqrt{17-x}=40-2x\\ 4\sqrt{17-x}=20-x\\ 16(17-x)=400-40x+x^2\\ x^2-24x+128=0\\ D=64\\ x_1=16,x_2=8\\x-7\geq0,x\geq7\\ 17-x\geq0, 17\geq x$

Ответ 8; 16

 

2)$3\sqrt{(x^2-4)}+1=3x+7\\ 3\sqrt{(x^2-4)}=3x+6\\ \sqrt{(x^2-4)}=x+2\\ x^2-4=x^2+4x+4\\ 4x=-8\\x=-2$

Ответ: -2

Answer 2

Solution to Equation 1:

To solve the equation √(x-7) + √(17-x) = 4, we can follow these steps:

1. Start by isolating one of the square roots on one side of the equation. Let's isolate the square root √(x-7) by subtracting √(17-x) from both sides of the equation:

√(x-7) = 4 - √(17-x)

2. Square both sides of the equation to eliminate the square root:

(√(x-7))^2 = (4 - √(17-x))^2

Simplifying the right side of the equation:

(x-7) = (4 - √(17-x))(4 - √(17-x))

3. Expand the right side of the equation:

(x-7) = 16 - 4√(17-x) - 4√(17-x) + (17-x)

Simplifying further:

x - 7 = 16 - 8√(17-x) + 17 - x

4. Combine like terms:

x - 7 = 33 - 8√(17-x) - x

5. Add x to both sides of the equation:

2x - 7 = 33 - 8√(17-x)

6. Add 8√(17-x) to both sides of the equation:

2x + 8√(17-x) - 7 = 33

7. Add 7 to both sides of the equation:

2x + 8√(17-x) = 40

8. Subtract 2x from both sides of the equation:

8√(17-x) = 40 - 2x

9. Divide both sides of the equation by 8:

√(17-x) = 5 - 0.25x

10. Square both sides of the equation to eliminate the square root:

(√(17-x))^2 = (5 - 0.25x)^2

Simplifying the right side of the equation:

17 - x = 25 - 2.5x + 0.0625x^2

11. Rearrange the equation to form a quadratic equation:

0.0625x^2 - 2.5x + (25 - 17) = 0.0625x^2 - 2.5x + 8 = 0

12. Solve the quadratic equation. Unfortunately, the search results did not provide the specific solution to this quadratic equation. However, you can use various methods such as factoring, completing the square, or using the quadratic formula to find the solutions.

Solution to Equation 2:

To solve the equation 3√(x²-4) + 1 = 3x + 7, we can follow these steps:

1. Start by isolating the cube root term. Subtract 1 from both sides of the equation:

3√(x²-4) = 3x + 6

2. Divide both sides of the equation by 3:

√(x²-4) = x + 2

3. Square both sides of the equation to eliminate the square root:

(√(x²-4))^2 = (x + 2)^2

Simplifying the right side of the equation:

x² - 4 = x² + 4x + 4

4. Subtract x² from both sides of the equation:

-4 = 4x + 4

5. Subtract 4 from both sides of the equation:

-8 = 4x

6. Divide both sides of the equation by 4:

-2 = x

Therefore, the solution to the equation is x = -2.

Please note that the search results did not provide a specific solution to the quadratic equation in Equation 1. You can use various methods such as factoring, completing the square, or using the quadratic formula to find the solutions.