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moneybird
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What are all the values of "x" between 0 and 2 pi that satisfy the equation?
\[(5+2\sqrt{6})^{\sin x} +(52\sqrt{6})^{\sin x} = 2 \sqrt{3}\]

Ishaan94
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oh wow

Walleye
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my exact thoughts. I have never seen anything like this

Ishaan94
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Hmm \[(5 + 2 \sqrt6)(5  2\sqrt6) = 25  24 =1\]

Ishaan94
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Okay I think maybe I got it!

Ishaan94
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Hmm
\[(5+2\sqrt{6})^{\sin x} +(\frac{1}{5 + 2\sqrt{6}})^{\sin x} = 2 \sqrt{3}\]
How about this? :D

moneybird
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o...

Ishaan94
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\[\frac{(5 + 2\sqrt{6})^{2\sin{x}} +1}{(5 + 2\sqrt{6})^{\sin{x}}} = 2\sqrt{3}\]
Are we getting somewhere? lol

moneybird
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I think I got it

Walleye
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awesome ishaan!

moneybird
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Let (5 + 2 sqrt (6)) be a
Let sinx be b
\[a^b + \frac{1}{a^b} = 2 \sqrt{3}\]
\[\frac{a^{2b} + 1}{a^b} = 2 \sqrt{3}\]
\[a^{2b} + 1  2 a^b \sqrt{3}\]

moneybird
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Let a^b be c
\[c^2 2c \sqrt{3} + 1 = 0 \]

Ishaan94
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\[(5 + 2\sqrt{6})^{2\sin{x}} + 1 = 2\sqrt{3}\times (5 + 2\sqrt{6})^{\sin{x}} \]
\[ 1 = 2\sqrt{3}\times (5 + 2\sqrt{6})^{\sin{x}}  (5 + 2\sqrt{6})^{2\sin{x}}\]
Hmm....

Ishaan94
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Oh i see what you did.... Hmm nice

moneybird
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Thanks for the hint :3

Ishaan94
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No Problem :)

moneybird
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x = 60, 150, 210, 330 degrees

Ishaan94
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Cool! :D
If only there was an easier way to get this

ali.athar
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\[\lim_{x \rightarrow 1} x ^{3}1/x ^{2}1\]

ali.athar
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is someone answer this limit question please

ali.athar
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ali.athar 0
limx→1x3−1/x2−1 someone solve this question

robtobey
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From Mathematica:\[\text{Limit}\left[x^3\frac{1}{x^2}1,x\to 1\right]=1 \]

ali.athar
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ali.athar 0
limx→1 x3−1/x2−1

ali.athar
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\[\lim_{x \rightarrow 2} x ^{3}8/x ^{2}+x ^{}6\]

moneybird
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x^3  8 = (x2) (x^2 + 2x + 4)
x^2 + x  6 = (x+3)(x2)
x2 cancels out
(x^2 + 2x + 4)/(x+3)
= (4 + 4 + 4 )/ 5
= 12/5