Answer :
To solve the equation √(3x) + 2 = 7x + √x, we’ll first isolate the radical terms and then square both sides of the equation to eliminate the radicals:
1. Subtract 2 from both sides to isolate the radicals:
√(3x) = 7x + √x - 2
2. Square both sides to eliminate the radicals:
[√(3x)]^2 = (7x + √x - 2)^2
3x = (7x + √x - 2)(7x + √x - 2)
3. Expand the right side:
3x = (49x^2 + 14x√x + 14x√x + x - 14x√x - 4√x - 14x√x - 4√x + 4)
4. Combine like terms:
3x = 49x^2 + 2x - 8√x + 4
5. Rearrange the equation to set it equal to zero:
49x^2 - x + 4 - 3x - 8√x = 0
6. Rewrite the equation in standard form:
49x^2 - 4x - 8√x + 4 = 0
This is a quadratic equation in terms of x and √x. To solve for x, we would typically use the quadratic formula, but this equation involves both x and √x, making it more complex. We may need to use numerical methods or algebraic manipulations to solve it further.
1. Subtract 2 from both sides to isolate the radicals:
√(3x) = 7x + √x - 2
2. Square both sides to eliminate the radicals:
[√(3x)]^2 = (7x + √x - 2)^2
3x = (7x + √x - 2)(7x + √x - 2)
3. Expand the right side:
3x = (49x^2 + 14x√x + 14x√x + x - 14x√x - 4√x - 14x√x - 4√x + 4)
4. Combine like terms:
3x = 49x^2 + 2x - 8√x + 4
5. Rearrange the equation to set it equal to zero:
49x^2 - x + 4 - 3x - 8√x = 0
6. Rewrite the equation in standard form:
49x^2 - 4x - 8√x + 4 = 0
This is a quadratic equation in terms of x and √x. To solve for x, we would typically use the quadratic formula, but this equation involves both x and √x, making it more complex. We may need to use numerical methods or algebraic manipulations to solve it further.
