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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.

Respuesta :

taskmasters
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.

meerkat18
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 =[tex] \sqrt{x} [/tex]. 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. 

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