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Question and Solution Template Learning Attribute(s) Included in Question : 1.4.2 Solve simple rational and radical equations in one variable and give examples showing how extraneous solutions may arise. Calculator Active? No Question : Which value of x satisfies following radical equation? √ x − 1 = x − 7 A) 5 B) 10 C) − 5 D) − 10 Equation Upload (Please write the text of the question along with the LaTeX Code): Which value of x satisfies following radical equation? $\sqrt{x-1}=x-7$ A) $5$ B) $10$ C) $-5$

D) $-10$ Correct answer: B On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult): 5 i Solution : Step 1 : Take square on both sides of the equation. ( √ x − 1 ) 2 = ¿ x − 1 = x 2 − 14 x + 49 Add or subtract the like terms and rewrite as a quadratic equation. x 2 − 15 x − 50 = 0 x 2 − 10 x − 5 x − 50 = 0 x ( x − 10 ) − 5 ( x − 10 ) = 0 ( x − 10 ) ( x − 5 ) = 0 x − 10 = 0 or x − 5 = 0 x = 10 or x = 5 Equation Upload (Please write the text of the question along with the LaTeX Code): \textbf{Step 1}: . Take square on both sides of the equation. $$(\sqrt{x-1})^{2} = (x-7)^{2}$$ $$x-1=x^2-14x+49$$ Add or subtract the like terms and rewrite as a quadratic equation. $$x^2-15x-50=0$$

So $$x=10$$ is the correct answer Step 3 : Substitute x = 5 into the equation. √ 5 − 1 ¿ √ 4 ¿ 2 And 5 − 7 ¿ − 2 So x = 5 isn’t the correct answer Equation Upload (Please write the text of the question along with the LaTeX Code): \textbf{Step 3}: Substitute $x=5$ into the equation. $$\sqrt{5-1}$$ $$=\sqrt{4}$$ $$=2$$ And $$5-7$$ $$=-2$$ So $$x=5$$ isn’t the correct answer