Which statement best reflects the solution(s) of the equation? √2x−1−x+2=0 answer choices: there is only one solution: x = 1. the solution x = 5 is an extraneous solution. there are two solutions: x = 1 and x = 5.  there is only one solution: x = 5. the solution x = 1 is an extraneous solution. there is only one solution: x = 5. the solution x = 0 is an extraneous solution.

There is only one solution: x = 5. The solution x = 1 is an extraneous solution.

Step-by-step explanation:

The given expression is

We rewrite the expression so that we equate everything to zero to obtain,

We now square both sides to obtain,

This simplifies to give us,

We now expand the parenthesis to get,

We now group the terms so that we can obtain the quadratic equation;

We split the middle term to obtain,

We factor to obtain,

Let us check to see whether  the two values satisfy the given equation.

When , we get,

This statement is false. Hence is an extraneous solution.

When , we get,

This statement is very trues.

Therefore is the only solution.

There is only one solution: x = 5. The solution x = 1 is an extraneous solution.

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