what does it mean to solve and check for extraneous solutions for sqry+9=1
You should write your equation as y^2 + 9 = 1.
First, solve your equation normally (by isolating y).
Then, to check for extraneous solutions, simply plug your answers into the original equation, and see if they check out. If one or more of your solutions does not work, then it is extraneous.
To solve the equation √(y+9) = 1, we need to isolate the variable y. Let's go through the steps:
Step 1: Square both sides of the equation to eliminate the square root:
(√(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
Now, we have solved the equation and found that y = -8. But we should also check for any potential extraneous solutions, which are solutions that arise during solving but do not satisfy the original equation.
To check for extraneous solutions, we substitute the found value of y (-8) back into the original equation √(y+9) = 1:
√(-8+9) = 1
√1 = 1
1 = 1
Since the left-hand side is equal to the right-hand side, we can say that our solution, y = -8, is valid and not an extraneous solution.
In conclusion, the solution to the equation √(y+9) = 1 is y = -8, and there are no extraneous solutions.