Question

What is the extraneous solution to the equation √√2p+1+2√√p-1?

Op=-4
Op=-2
Op=0
Op=4

Answer 1

To find the extraneous solution to the given equation, simplify and solve it, and check if the obtained solution satisfies the original equation.

Step-by-step explanation:

To find the extraneous solution to the equation √√2p+1+2√√p-1, we need to solve the equation and check if the obtained solutions satisfy the original equation. Let's solve the equation:

1. Start by simplifying the equation by applying the innermost square root and then the outermost square root. √√2p+1 becomes √(2p+1) and 2√√p-1 becomes 2√(p-1).
2. Combine the simplified terms: √(2p+1)+2√(p-1).
3. Set the expression equal to zero: √(2p+1)+2√(p-1) = 0.
4. Now, square both sides to eliminate the square roots: (√(2p+1))^2+(2√(p-1))^2 = 0^2.
5. Simplify and solve the resulting equation: 2p+1+4(p-1) = 0.
6. Expand and combine like terms: 2p+1+4p-4 = 0.
7. Combine like terms again: 6p-3 = 0.
8. Add 3 to both sides: 6p = 3.
9. Divide by 6: p = 3/6.
10. Reduce the fraction: p = 1/2.

So, the solution to the equation is p = 1/2. To check if it is an extraneous solution, plug it back into the original equation: √√2(1/2)+1+2√√1/2-1. Simplifying this expression, we get 0+1+2(0) = 1. Since 1 is not equal to zero, the obtained solution p = 1/2 is not an extraneous solution.

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