Solve the equation. Check both solutions and only write the real solution.
the square root of 6m minus 5 = m
A. {1}
B. {5}
C. {1, 5}
D. no real solution
I think its B
√(6m) - 5 = m
√(6m) = m+5
square both sides
6m = m^2 + 10m + 25
m^2 + 4m + 25 = 0
m = (-4 ± √-84)/2
no real solution
if you think it is B), why not check it
LS = √30 - 5
RS = 5
mmmhhh
However, if you meant:
√(6m-5) = 5
then 6m-5 = 25
6m = 30
m = 5
See what happens if you don't use brackets to avoid ambiguity?
U tried bt itz wrong . .ansa iz a . . 6m - 5 =m . Colect lyk terms . 6m -m =5 . 5m =5 . Then m =1 .
To solve the equation √(6m - 5) = m, you can follow these steps:
Step 1: Square both sides of the equation to eliminate the square root, since squaring will undo the square root.
(√(6m - 5))^2 = m^2
Simplifying: 6m - 5 = m^2
Step 2: Rearrange the equation to bring all terms to one side, making it a quadratic equation:
m^2 - 6m + 5 = 0
Step 3: Factorize or use the quadratic formula to solve for m. In this case, the quadratic equation can be factored as:
(m - 5)(m - 1) = 0
So, either m - 5 = 0 or m - 1 = 0.
Solving each equation separately:
If m - 5 = 0, then m = 5
If m - 1 = 0, then m = 1
Therefore, the possible solutions are m = 1 and m = 5.
However, to find the real solution, we need to substitute both values back into the original equation and check if it holds.
Checking m = 1:
√(6(1) - 5) = 1
√(1) = 1
1 = 1 (True)
Checking m = 5:
√(6(5) - 5) = 5
√(30 - 5) = 5
√(25) = 5
5 = 5 (True)
Both solutions pass the check, so the real solution to the equation is m = 1.
Therefore, the correct answer is A. {1}.