Solving Fractions with Roots: an Example

AI Thread Summary
The discussion revolves around simplifying the expression (3 + √24) / (2 + √6) into the form a + b√c / d. The user initially struggles with the simplification process, particularly with the square root of 144. After realizing that √144 equals 12, they express relief and acknowledge having overcomplicated the problem. The conversation highlights the common challenge of working with fractions involving roots and the importance of breaking down steps clearly. Overall, the user feels more confident to continue after receiving clarification.
james_rich
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Hey having a bit of trouble with this question, not sure what to do!

QUESTION - express the fraction in the form a + b rootc / d


3 + root24 / 2 + root6

------------------------------------------
(3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6)

Simplifying gives

(6 - 3root6 + 2root24 - root144) / -2

(6 - 3root6 + 2 x 2root6 - root144) /-2

is this right so far? the problem i am having is simplifying the root144 to a root6 inequality!
 
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HINT: \sqrt {144} = 12
 
D'oh! that is so easy!

I think i tried to over complicate it! My Brain hurts! I've stared at this piece of paper for the last 10mins!

Thanx a lot, i can carry on now!

Forgive the stupidity!
 

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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