The discussion revolves around finding the number of solutions to the equation $$\sqrt {x^2}-\sqrt {(x-1)^2} + \sqrt {(x-2)^2}=\sqrt {5}$$, which involves understanding the properties of square roots and absolute values in the context of quadratic equations.
Some participants have identified that the equation can be rewritten using absolute values, leading to a clearer path for solving it. Guidance has been provided regarding plotting the function to visualize the solutions.
Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can receive. There is an ongoing exploration of the assumptions related to the properties of square roots and absolute values.
What is the square root of the square of a number ? ##\sqrt{a^2} = ?##Wrichik Basu said:
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 said:
##\sqrt{a^2} = |a|##, that much I know. And the others are both 3.ehild said:
You mean to say that the expression reduces to ## |x|-|x-1|+|x-2|=\sqrt {5}##?ehild said:
Yes, it is correct. Just plot the function, and see, if it can take the value √5, and how many times.Wrichik Basu said:
Right, plot on a number line and... I understood. Thank you, sir.ehild said:
Thank you.ehild said: