Summer Math review: Solve for z

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To solve for z in the equation y^2 + 3yz - 8z - 4x = 0, the correct rearrangement yields z = (y^2 - 4x) / (3y - 8). Initially, there was confusion about the sign of the answer, but it was clarified that the negative was incorrect. The term "alienate" was humorously noted as an unusual way to describe isolating z. This discussion highlights the importance of careful algebraic manipulation in solving equations. Clear communication of mathematical processes can lead to better understanding among peers.
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Homework Statement


solve for z:
y^2+3yz-8z-4x=0

Homework Equations


The Attempt at a Solution


I tried to alienate the z
I got the answer:
z=(y^2-4x)/(3y-8)
 
Last edited:
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nevermind, i got the answer
 
Then I presume you realized you had the negative of the correct answer.
 
Heqi said:
I tried to alienate the z

haha first time I've seen anyone describe it that way
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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