Question

1.Create an equation that results in at least one extraneous solution. Work through your equation, justify each step, and explain how the solution is extraneous.

Answer 1

Extraneous solutions are roots of the polynomial which when substituted to the expression, the expression is invalid or not true. One example is x - 6 =
`√(x)`. We square both sides, x^2 - 12x + 36 = x. x^2 - 13x + 36 = 0. This is equal to (x-4)*(x-9) = 0. The roots are 9 and 4. The extraneous solution is 4 since when we substitute 4 to the original expression, there is no equality.

Answer 2

In math, an extraneous solution is a solution of an equation that is obtained from solving the problem however this solution is not a valid solution. For instance,
(1/(x − 2)) + (1/(x + 2)) = 4 / (x − 2)(x + 2)

[(x − 2)(x + 2)/(x − 2)] + [(x − 2)(x + 2)/(x + 2)] = [4(x − 2)(x + 2)] / [(x − 2)(x + 2)]

(x−2)+(x+2)=4
x = 2

But 2 is excluded from the domain of the original equation because it would make the denominator of one zero and this is not valid.