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

[Kartik.]

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?

 

[DonAntonio]

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:

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

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

DonAntonio

 

[Kartik.]

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

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

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.