Solving equations and finding solution set

AI Thread Summary
To solve the equation 3 sin(x) - 6 = sin(x) - 5 in the interval [0, 2π), first rearrange it to set it equal to zero. This leads to the equation 2 sin(x) - 1 = 0, which simplifies to sin(x) = 1/2. The solutions for sin(x) = 1/2 in the specified interval are x = π/6 and x = 5π/6. The discussion highlights the importance of correctly rearranging and simplifying equations to find solutions effectively. Understanding the substitution of sin(x) with a variable can also aid in solving similar problems.
AlisonWagner
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Homework Statement


Solve the equation in the interval [0,2∏)
3 sinx-6 = sinx-5


Homework Equations





The Attempt at a Solution


I originally tried to set it equal to zero and then divide by the 3 and then factor out the sinx but I didn't think that made any sense? HELP!
 
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suppose sin(x) was called X. How would you then solve the problem?
 
Ooh! I totally got it now! I was completely stuck until you said that. Thanks!
 

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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