u-2√u=3. what is u?
change u to x^2, then sqrtu = x
x^2-2x-3=0
(x-3)(x+1)=0
x=3, or u= + 9
x=-1, or u=+ 1
checking
u=9
9-2*3=3 checks
u= i
1-2 does not equal 3, does not check.
To solve the equation u - 2√u = 3, we can follow these steps:
Step 1: Move the term with the square root to one side of the equation.
u - 3 = 2√u
Step 2: Square both sides of the equation to eliminate the square root.
(u - 3)^2 = (2√u)^2
u^2 - 6u + 9 = 4u
u^2 - 10u + 9 = 0
Step 3: Solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:
(u - 1)(u - 9) = 0
Step 4: Set each factor equal to zero and solve for u:
u - 1 = 0 or u - 9 = 0
u = 1 or u = 9
Therefore, the values of u that satisfy the equation u - 2√u = 3 are u = 1 and u = 9.