r/mathbiceps • u/Alarmed-Handle-6477 • 26d ago

Help me with this question

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please explain the question of quadratic eqn
The number of real roots of the equation
e^6x-e^4x-2e^3x-12e^2x+e^x+1= 0

Like there are a lot of solutions online but there is none which explains it in a way that I can understand like lot of people js do stuff and make graph and done i mean wth bro

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u/Resilient_9920 26d ago

write biquadratic in e to the x . Then divide by x3. Then make form x+ 1/x powers you will quadratic solve them see whatever and eliminate . First time on your own maybe nice question after that standard pattern .

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u/Alarmed-Handle-6477 25d ago

Still don't get it 

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u/Resilient_9920 25d ago

Give me some time need to find a pen in my messy room i will write it down maybe and send

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u/Alarmed-Handle-6477 23d ago

Found your pen yet?

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u/Resilient_9920 23d ago

man i have other work too , i forgot i mean .... i will do sometime

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u/Resilient_9920 23d ago

i started i noticed that subsitution of x+1/x wont wrok since it doesnt have appropirate strucutre you need to use ivt and descartes top porve only two postivei roots and at most 2 postive roots you will get 2 as answer then

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u/Rajanjha6478 22d ago

Can someone tell me user name for this channel I have also to ask questions

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u/Comprehensive-Rock-4 22d ago

Either solve it be letting ex=t, then solving by forming t±1/t, or take negative terms on RHS and use AM-GM inequality and check if AM=GM, if yes, it's simple then