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What is the solution of the equation √2-2=2-4?Enter your answer in the box.A. 6B. 10C. 11OD.4
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What is the solution of the equation √2-2=2-4?Enter your answer in the box.A. 6B. 10C. 11OD.4

What is the solution of the equation √2-2=2-4?Enter your answer in the box.A. 6B. 10C-example-1
User Rahul Agarwal
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1 Answer

21 votes
21 votes

ANSWER:

A. 6

Explanation:

We have the following equaton:


√(x-2)=x-4

We solve for x:


\begin{gathered} \left(√(x-2)\right)^2=\left(x-4\right)^2 \\ \\ x-2=x^2-8x+16 \\ \\ x^2-8x+16=x-2 \\ \\ x^2-8x+16-x+2=0 \\ \\ x^2-9x+18=0 \\ \\ \left(x-3\right)\left(x-6\right)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x-6=0\operatorname{\rightarrow}x=6 \\ \\ \text{ We check each solution, like this:} \\ \\ √(6-2)=6-4\rightarrow√(4)=2\rightarrow2=2\rightarrow\text{ True} \\ \\ √(3-2)=3-4\rightarrow√(1)=-1\rightarrow1=-1\rightarrow\text{ False} \end{gathered}

That means that the only solution of the equation is x = 6.

Therefore, the correct answer is A. 6

User Nathan Rice
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3.3k points
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