Solve: √2a−1=a−8
Select one:
a. a=13
b. a=−7
c. a=5,13
d. a=−5,−13
Responses (2)
let a = 13. The square root of 2a-1 is the square root of 25, which is 5; 13-8 also equals 5 so it could be option (a).
If a was a negative number, the square root of it would be an imaginary number, so it's not (b).
Let a = 5. The square root of 2a-1 is the square root of 9, which is 3. 5-8 is -3, so it can't be (c).
For the same reason it can't be (b), it also isn't (d).
Therefore I would suggest that the correct answer is (a) a = 13.
Hope this helps (and that it's correct!!)
Solve: √(2)a − 1 = a − 8 No solution
Solve: √(2a) − 1 = a − 8 No solution
Solve: √(2a − 1) = a − 8
We use parentheses to indicate what acts on what. If you don't present a problem correctly, people have to guess at what you are talking about. You can not stand a spelling mistake in math.
um
I should have shown you how to solve that.
√(2a − 1) = a − 8 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Square both sides.
2a - 1 = a^2 - 16a + 64 Simplify.
a^2 - 18a + 65 = 0 Study this page until it seems obvious:
en.wikipedia.org/wiki/Polynomial_remainder_theorem
A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.
(a - 5)(a - 13) = 0
a = 5, 13 Now you have a snake in the deal. That means you are going to get bit if you don't watch out. When you squared both sides you introduced a phony solution. So you have to be sure that your answer actually works in the original statement. Only 13 works in the original statement. If ever you have to divide by the variable to find an answer, that obscures a valid solution.
www.wolframalpha.com/input/?i=a^2+-+18a+%2B+65+%3D+0
Bookmark the site to check all your homework.
omg thank you so much