# A problem in Quadratic Equations

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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