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3z-1+2√z=32This equation gets solved when we assume the z as

by Kartik.
Tags: 2√z32this, assume, equation, solved
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Kartik.
#1
May4-12, 10:14 AM
P: 55
3z-1+2√z=32
This equation gets solved when we assume the z as any variable's2 and turn that into a quadratic form.
Is there any other way of solving this equation?
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DonAntonio
#2
May4-12, 10:29 AM
P: 606
Quote Quote by Kartik. View Post
3z-1+2√z=32
This equation gets solved when we assume the z as any variable's2 and turn that into a quadratic form.
Is there any other way of solving this equation?


Well, when we square stuff, which ammounts to basically the same thing:

[itex]3z-33=-2\sqrt{z}\Longrightarrow 9z^2-198z+1089=4z\Longrightarrow 9z^2-202z+1089=0\Longrightarrow z_1=13.444\,,\,\,z_2=9[/itex] .

As many times with these exercises, only the second number above is a solution to the original equation.

DonAntonio
Kartik.
#3
May4-12, 11:21 AM
P: 55
Quote Quote by DonAntonio View Post
Well, when we square stuff, which ammounts to basically the same thing:

[itex]3z-33=-2\sqrt{z}\Longrightarrow 9z^2-198z+1089=4z\Longrightarrow 9z^2-202z+1089=0\Longrightarrow z_1=13.444\,,\,\,z_2=9[/itex] .

As many times with these exercises, only the second number above is a solution to the original equation.

DonAntonio
Thanks :D
But, the assumption thing looks simple enough.


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