Question

Solve x+x/sqrt x^2-1 = 2sqrt2

Answer 1

2x^2+x√(3x^2+1) = 4

x√(3x^2+1) = 4 - 2x^2
x^2 (3x^2+1) = 16 - 16x^2 + 4x^4
x^4 - 17x^2 + 16 = 0
(x^2-16)(x^2-1) = 0
x = ±1, ±4
But only x = -4,1 satisfy the original equation

Answer 2

2(x^2)+xsqrt3x^2+1 = 4

Answer 3

Oops

Answer 4

That was my question 😓

Answer 5

[AI-generated answer — Explain Bot]

To solve the equation, x + x/√(x^2 - 1) = 2√2, we can go through the following steps:

Step 1: Simplify the equation:
Multiply both sides of the equation by √(x^2 - 1) to eliminate the denominator.
This gives us: √(x^2 - 1) * x + x = 2√2 * √(x^2 - 1)

Step 2: Simplify the equation further:
Distribute √(x^2 - 1) to x, and simplify the right side:
x√(x^2 - 1) + x = 2√2√(x^2 - 1)
x√(x^2 - 1) + x = 2√2(x^2 - 1)

Step 3: Expand the equation:
Squaring both sides of the equation will simplify and remove the square root terms:
(x√(x^2 - 1) + x)^2 = (2√2(x^2 - 1))^2

Step 4: Simplify after expanding:
(x^2(x^2 - 1) + 2x√(x^2 - 1) + x^2) = (4 * 2 * (x^4 - 2x^2 + 1))

Step 5: Continue simplification:
x^4 - x^2 + 2x√(x^2 - 1) + x^2 = 8x^4 - 16x^2 + 8

Step 6: Rearrange the equation:
Combine like terms on both sides:
x^4 - 17x^2 + 8 = 2x√(x^2 - 1)

Step 7: Isolate the radical term:
Move the radical term to one side of the equation and the remaining terms to the other side:
x^4 - 17x^2 + 8 - 2x√(x^2 - 1) = 0

Step 8: Solve the equation:
Now, we can solve the equation either by factoring or using numerical methods such as graphing or approximation methods.