I need help with: solving and check for extraneous solutions.
sqrt y+9=1
Is your equation √(y+9) = 1?
I'll assume it is...
First, square both sides to get
y + 9 = 1
y = -8
Now plug that back into the original equation to see if it is extraneous. (An extraneous solution is one that does not work.)
√(-8 + 9) = 1
√(1) = 1
That is correct, so the answer is y = 1.
To solve the equation sqrt(y + 9) = 1, we need to isolate the variable y. Here are the steps to solve this equation:
Step 1: Square both sides of the equation to eliminate the square root:
(sqrt(y + 9))^2 = 1^2
y + 9 = 1
Step 2: Subtract 9 from both sides of the equation:
y + 9 - 9 = 1 - 9
y = -8
Therefore, the solution to the equation is y = -8.
To check for extraneous solutions, we need to substitute the obtained solution back into the original equation and see if it satisfies the equation. Let's check:
sqrt(y + 9) = 1
Substituting y = -8:
sqrt((-8) + 9) = 1
sqrt(1) = 1
The square root of 1 is indeed 1.
Therefore, we verified that the obtained solution y = -8 is a valid solution and there are no extraneous solutions.