What is missing of the binominal in the following:
(radical 3 minus 2) ( ?) = -1
To determine the missing term in the binomial expression, we need to solve the equation:
(sqrt(3) - 2) * (x) = -1
To isolate the missing term, we will solve the equation step by step:
Step 1: Distribute the binomial
(sqrt(3) - 2) * (x) = -1
sqrt(3) * x - 2x = -1
Step 2: Rearrange the equation
sqrt(3) * x - 2x + 1 = 0
Step 3: Combine like terms
(x * sqrt(3) - 2x) + 1 = 0
x(sqrt(3) - 2) + 1 = 0
Now, we need to isolate x(sqrt(3) - 2) to solve for x.
Step 4: Move the constant term to the other side
x(sqrt(3) - 2) = -1 - 1
Step 5: Simplify the equation
x(sqrt(3) - 2) = -2
Now, to solve for x, we can divide both sides of the equation by (sqrt(3) - 2).
Step 6: Divide both sides by (sqrt(3) - 2)
x = -2 / (sqrt(3) - 2)
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt(3) + 2):
Step 7: Rationalize the denominator
x = (-2 / (sqrt(3) - 2)) * ((sqrt(3) + 2) / (sqrt(3) + 2))
x = (-2 * (sqrt(3) + 2)) / ((sqrt(3) - 2) * (sqrt(3) + 2))
x = (-2 * sqrt(3) - 4) / (3 - 2^2)
x = (-2 * sqrt(3) - 4) / (3 - 4)
x = (-2 * sqrt(3) - 4) / (-1)
x = 4 + 2 * sqrt(3)
Therefore, the missing term in the binomial expression is 4 + 2 * sqrt(3).