Solve. Express your answer as exact roots.
(s+6)^2 = 3/4
Sq root (s+6)^2 = +-sq root 3/4
(s+6) = sq root 3/ 2
s = -6 +- sq root 3
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2
(The answer according to the textbook is (-12 +- sq root 3)/2. What error have I made?)
Thank you
(s+6)^2 = 3/4
s+6 = ±√3/2
s = -6±√3/2
This is where it helps to keep track of things
s = -6 ± (√3/2)
NOT
s = (-6±√3)/2
so, putting it all over 2,
s = (-12±√3)/2
Thank you!
It seems like the error in your solution lies in the step where you take the square root of both sides of the equation. Let's go through the correct steps:
Starting with:
(s + 6)^2 = 3/4
Taking the square root of both sides:
sqrt((s + 6)^2) = sqrt(3/4)
Here, it's important to remember that when taking the square root of a squared term, you need to consider both the positive and negative square roots:
(s + 6) = ± sqrt(3/4)
Now, simplify the square root of 3/4:
(s + 6) = ± sqrt(3)/sqrt(4)
Since the square root of 4 is 2:
(s + 6) = ± sqrt(3)/2
At this point, you need to isolate s:
s = -6 ± sqrt(3)/2
Rationalizing the denominator by multiplying both the numerator and denominator by 2:
s = -6 ± sqrt(3)(2)/2(2)
This gives you the correct solution:
s = -6 ± sqrt(3)/2
So, the correct answer is (-6 ± sqrt(3))/2. The textbook's answer of (-12 ± sqrt(3))/2 seems to be incorrect.