Solve: t - sqrt () 6t - 9 = 0
a) {-3}
b) {-3,3}
c) 0
d) {3}
Did you mean
t - √(6t-9) = 0 ?
if so, then
t = √(6t-9)
square both sides
t^2 = 6t-9
t^2 - 6t + 9 - 0
(t-3)^2 = 0
t-3 = 0
t = 3
yes i did and thanks and how do i put that like you have
to create √ symbol
on a PC, hold down the Alt key, and at the same time press 251 on the number pad, then release the Alt key
on Mac,
hold down the Option key, and press V, release the Option key
To solve the equation t - sqrt(6t - 9) = 0, we need to isolate the variable t. Here's how we can do it step by step:
1. First, let's move the square root term to the other side of the equation by adding sqrt(6t - 9) to both sides:
t = sqrt(6t - 9)
2. Now, let's square both sides of the equation to eliminate the square root:
t^2 = (sqrt(6t - 9))^2
t^2 = 6t - 9
3. Rearranging the equation, we get a quadratic equation in terms of t:
t^2 - 6t + 9 = 0
4. This quadratic equation can be factored as (t - 3)(t - 3) = 0, which simplifies to (t - 3)^2 = 0.
5. Setting (t - 3)^2 = 0 implies that t - 3 = 0, since the square of any non-zero number is positive.
Solving for t, we find t = 3.
Therefore, the solution to the equation t - sqrt(6t - 9) = 0 is t = 3. The correct answer is option d) {3}.