A problem in Quadratic Equations

[Wrichik Basu]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Completely clueless as to where to start.

 

[ehild]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Completely clueless as to where to start.

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

 

[ehild]

Homework Statement

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

.

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?

 

[Wrichik Basu]

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?

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

 

[Wrichik Basu]

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?

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.

 

[ehild]

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.

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

 

[Wrichik Basu]

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

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

 

[ehild]

Well, this is the plot

 

[Wrichik Basu]

Well, this is the plot

View attachment 204036

Thank you.