MHB Is this theory regarding the graph and the square root valid?

AI Thread Summary
The discussion centers on a method for finding square roots using a graph of the quadratic equation x^2 - 2x - 3. A participant claims to have discovered a technique to derive the square root of any number by substituting it into the equation. However, another contributor points out a logical inconsistency in the approach, noting that if x equals the square root of 3, it cannot simultaneously satisfy the equation derived from the substitution. This raises questions about the validity of the proposed theory regarding the relationship between the graph and square roots. Ultimately, the validity of the method remains contested within the discussion.
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http://mathhelpboards.com/pre-algebra-algebra-2/find-value-squareroot-3-using-graph-drawing-suitable-straight-line-19973.html

greg1313 said:
Mathematics is a science and experimentation is a valuable tool. The first thing I did was to substitute $\sqrt3$ for $x$ in the given quadratic and observe the results. Get your hands dirty!
I guess I found a method to obtain the square root of any number using the above graph.

$x^2-2x-3$ What I did to find the square root of 3 was replace $x^2$ with the desired square root

$\sqrt{3}^2-2x-3=3-2x-3=-2x=0=y$

And check this out if we replace the $x^2$ of the formula of the formula to obtain a square root of any number

$\sqrt{7}^2-2x-3=7-2x-3=-2x+4=0=y$

Check the $x$ axis of the intersection point of the graph and the x axis

Is this theory regarding the graph and the square root really valid?

[graph]z0awzx3ity[/graph]
 
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Re: An amazing discovery regarding the graph and the square root

mathlearn said:
$\sqrt{3}^2-2x-3=3-2x-3=-2x=0=y$
If [math]x = \sqrt{3}[/math] then [math]x^2 - 2x - 3 = (\sqrt{3})^2 - 2 \sqrt{3} - 3[/math]. You have to replace all the x's.

Also: [math]\sqrt{3}^2-2x-3=3-2x-3=-2x=0[/math] says that -2x = 0, but you originally had [math]x = \sqrt{3}[/math], which both can't be true.

-Dan
 
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