y=u+1/u+2 solve for "u".
Please help me :)
I suspect that you mean
y = (u+1) / (u+2)
y u + 2 y = u + 1
y u - u = 1 - 2 y
u ( y - 1 ) = (1 - 2 y)
u = (1-2 y)/(y-1)
Thank you!!
To solve the equation for "u", we need to isolate the variable on one side of the equation. Let's go step by step:
1. Start with the given equation: y = u + 1/u + 2.
2. Multiply through by "u" to eliminate the fraction:
yu = u^2 + 1 + 2u.
3. Rearrange the equation by moving all terms to one side:
u^2 + 2u - yu - 1 = 0.
4. Combine like terms:
u^2 + (2 - y)u - 1 = 0.
5. Now, we have a quadratic equation in terms of "u". We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula here:
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac))/(2a).
In our case, we have a = 1, b = (2 - y), and c = -1:
u = (-(2 - y) ± √((2 - y)^2 - 4(1)(-1)))/(2(1)).
6. Simplify the equation:
u = (-2 + y ± √(4 - 4y + y^2 + 4))/(2).
u = (-2 + y ± √(y^2 - 4y + 4))/(2).
7. Now, we have two solutions for "u" in terms of "y":
u₁ = (-2 + y + √(y^2 - 4y + 4))/(2).
u₂ = (-2 + y - √(y^2 - 4y + 4))/(2).
So, the solutions for "u" are u₁ and u₂.