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1. May 18, 2017

Wrichik Basu

• Member warned that some effort must be shown
1. The problem statement, all variables and given/known data

Find the number of solutions of the equation $$\sqrt {x^2}-\sqrt {(x-1)^2} + \sqrt {(x-2)^2}=\sqrt {5}$$

2. Relevant equations

3. The attempt at a solution

Completely clueless as to where to start.

Last edited: May 18, 2017
2. May 18, 2017

ehild

What is the square root of the square of a number ? $\sqrt{a^2} = ?$

Last edited: May 18, 2017
3. May 22, 2017

ehild

Write the equation without square roots and squares. Do you know what is $\sqrt{3^2}$? and $\sqrt{(-3)^2}$? And what is $\sqrt{a^2}$ in general?

4. May 22, 2017

Wrichik Basu

$\sqrt{a^2} = |a|$, that much I know. And the others are both 3.

5. May 22, 2017

Wrichik Basu

You mean to say that the expression reduces to $|x|-|x-1|+|x-2|=\sqrt {5}$?

Then I can solve it without problem, just tell if my evaluation is correct.

6. May 22, 2017

ehild

Yes, it is correct. Just plot the function, and see, if it can take the value √5, and how many times.

7. May 22, 2017

Wrichik Basu

Right, plot on a number line and... I understood. Thank you, sir.

8. May 22, 2017

ehild

Well, this is the plot

Last edited: May 22, 2017
9. May 23, 2017