# plz help

• Jul 18th 2006, 11:41 AM
bobby77
plz help
1>Is sqrt(x^2)=x an identity (true for all values of x)?

2> For the equation x-sqrt(x)=0 , perform the following:
a) Solve for all values of x that satisfies the equation.
b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

c) How does the graph relate to part a?
• Jul 18th 2006, 11:53 AM
Quick
Quote:

Originally Posted by bobby77
1>Is sqrt(x^2)=x an identity (true for all values of x)?

No, it isn't true if x is less than 0
• Jul 18th 2006, 12:12 PM
earboth
Quote:

Originally Posted by bobby77
1>Is sqrt(x^2)=x an identity (true for all values of x)?

the square root is per definition a positive number or zero. x can be a negative number. So the answer is NO.

$\sqrt{(-3)^2}\neq (-3)$

Quote:

Originally Posted by bobby77
2> For the equation x-sqrt(x)=0 , perform the following:
a) Solve for all values of x that satisfies the equation.

factorize the lhs of this equation:
$x-\sqrt{(x)}=0 \Longrightarrow \sqrt{x}(\sqrt{x}-1)=0$
Thus: $\sqrt{x}=0\ \vee\ \sqrt{x}=1$. Therefore x = 0 or x = 1.

Quote:

Originally Posted by bobby77
b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
c) How does the graph relate to part a?

I am not certain what you mean by functions (plr!). So I made a diagram of g(x)=x and w(x)=sqrt(x). the x-values of the intercepts are the solutions of the equation.

Bye

EB
• Jul 18th 2006, 12:33 PM
ThePerfectHacker
Quote:

Originally Posted by bobby77
1>Is sqrt(x^2)=x an identity (true for all values of x)?

Let me add that $\sqrt{x^2}=|x|$

Prove: If $x\geq 0$ then $\sqrt{x^2}=x$ because $x^2=x^2$, and $|x|=x$ so that is true.
If $x<0$ then $\sqrt{x^2}=-x$ because $(-x)^2=x^2$ and $-x\geq 0$, and $|x|=-x$ so that is true.

Thus, $\sqrt{x^2}=|x|$