Question

√(x^2+1-2x) -6√(x-1) = 7

Answer 1

Ответ:

50

Пошаговое объяснение:

√(x^2+1-2x) -6√(x-1) = 7

(√(x-1))^2-6√(x-1)=7

пусть√(x-1)=а, где а положительно или равно нулю,

а^2-6а-7=0

а1+а2=6        

а1*а2=-7

а1=7    

а2=-1  - посторонний по усл см выше, тогда

 √(x-1)=7

x-1=49

х=50

Answer 2

To solve the equation √(x^2 + 1 - 2x) - 6√(x - 1) = 7, follow these steps:

Step 1: Start by isolating one of the square roots on one side of the equation. Let's isolate the first square root term: √(x^2 + 1 - 2x).

Add 6√(x - 1) to both sides of the equation:

√(x^2 + 1 - 2x) = 7 + 6√(x - 1)

Step 2: Square both sides of the equation to eliminate the square root on the left side:

(x^2 + 1 - 2x) = (7 + 6√(x - 1))^2

Simplify the right side of the equation:

x^2 + 1 - 2x = 49 + 84√(x - 1) + 36(x - 1)

Step 3: Combine like terms on the right side:

x^2 - 2x + 1 = 85 + 84√(x - 1) + 36x - 36

Step 4: Move all terms involving x to one side of the equation and the constants to the other side:

x^2 - 2x - 36x = 85 + 84√(x - 1) - 36 - 1

Simplify:

x^2 - 38x = 48 + 84√(x - 1)

Step 5: Factor out x from the left side:

x(x - 38) = 48 + 84√(x - 1)

Step 6: Isolate the square root term by subtracting 48 from both sides:

x(x - 38) - 48 = 84√(x - 1)

Step 7: Square both sides of the equation to eliminate the square root:

(x(x - 38) - 48)^2 = (84√(x - 1))^2

Expand the left side:

x^2(x - 38)^2 - 96x(x - 38) + 48^2 = 7056(x - 1)

Step 8: Simplify and expand further:

x^2(x^2 - 76x + 1444) - 96x^2 + 3648x + 2304 = 7056x - 7056

x^4 - 76x^3 + 1444x^2 - 96x^2 + 3648x + 2304 = 7056x - 7056

Step 9: Rearrange terms and simplify:

x^4 - 76x^3 + 1348x^2 - 3648x - 9360 = 0

Step 10: At this point, the equation becomes a quartic equation which can be difficult to solve directly. You may need to use numerical methods or a graphing calculator to approximate the solutions.

Please note that this solution involves multiple steps and algebraic manipulations. Check your work and calculations carefully, as mistakes can easily be made along the way. Additionally, solving quartic equations can be complex, so using numerical methods or technology might be necessary to find accurate solutions.