MATH SOLVE

5 months ago

Q:
# is the solution of this equation extraneous?

Accepted Solution

A:

Answer:x = - 3 is extraneousStep-by-step explanation:Given[tex]\sqrt{x+7}[/tex] - 1 = x Β ( add 1 to both sides )[tex]\sqrt{x+7}[/tex] = x + 1 ( square both sides )x + 7 = (x + 1)Β² β distribute right sidex + 7 = xΒ² + 2x + 1 ( subtract x + 7 from both sides )0 = xΒ² + x - 6 β in standard form0 = (x + 3)(x - 2) β in factored formEquate each factor to zero and solve for xx + 3 = 0 β x = - 3x - 2 = 0 β x = 2As a checkSubstitute these values into the equation and if both sides are equal then they are the solutions.x = - 3 : [tex]\sqrt{-3+7}[/tex] - 1 = [tex]\sqrt{4}[/tex] - 1 = 2 - 1 = 1 β - 3x = 2 : [tex]\sqrt{2+7}[/tex] - 1 Β = [tex]\sqrt{9}[/tex] - 1 = 3 - 1 = 2x = 2 is a solution and x = - 3 is extraneous