The equation 3z - 1 + 2√z = 32 can be solved by transforming it into a quadratic form. By assuming z as a variable squared, the equation simplifies to 9z² - 202z + 1089 = 0. The solutions derived from this quadratic equation yield z₁ = 13.444 and z₂ = 9, with only z₂ being a valid solution to the original equation. This method highlights the importance of careful manipulation of equations in algebraic problem-solving.
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Well, when we square stuff, which ammounts to basically the same thing:Kartik. said: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?
Thanks :DDonAntonio said: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