Do you know this simple trick? | Solve for (x^3)+(1/x^3) | Math Olympiad Preparation

[@mahinnazu5455]

Really so nice maths

[@PreMath]

Thanks for liking You are awesome. Keep it up 👍

[@Aligakore]

Excellent ! I have done it the very long way just for fun after watching the video (calculate Delta to solve for x and then calculate (x^3)+(1/x^3) for both solutions of the equation). Your trick is definitely great 😅 Thank you !

[@PreMath]

Glad it helped! You are awesome. Keep it up 👍

[@anthonycheng1765]

solve equation x=0.5*(3 plus/minus sqrt(5)). Add 8 on both sides to get x^2-3x+9=8, multiply both sides by x+3 to get x^3+27=8(x+3),x^3=8x-3. x^3=9 plus/minus 4*sqrt(5). then performing rationalization x^3+1/x^3 = 18.

[@GetMatheFit]

Great work 👌👍🔝 You are my hero. Keep going on.

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!

[@PreMath]

Thank you too You are awesome. Keep it up 👍

[@dirklutz2818]

So simple! Of course, I did it the long and hard way.

[@devondevon4366]

You could also x -3 + 1/x =0 divide both sides by 3 x+1/x = 3 x + 1/x ---------- x^2 + 1/x^2 + 1/x*x + x/*1/x = 9 (square x+1/x) x^2 + 1/x^2 + 2 =9 x^2 + 1/x^2 = 7 x + 1/x = 3 (multiply x^2 + 1/x^2 by x + 1/x) ----------------------- x^3 + 1/x^3 + 1/x +x = 21 x^3 + 1/x^3 + 3 = 21 (substitute the value for 1/x + x =3) x^3 + 1/x^3 = 21-3 =18 I did it this way first to make sure the answer was correct, then I used identity to do it the other way, then post it first.

[@devondevon4366]

18 x+1/x = 3 divided both sides by x, then add 3 to both sides (x+1/x)^3 = 27 cube both sides x^3 + 1/x^3 + 3* x*1/x( x+ 1/x) = 27 x^3 + 1/x*3 + 3(3) =27 x^3 + 1/x^3 = 27-9 =18 answer

[@adgf1x]

=>x^2+1=3x=>x^2/x+1/x=3=>(x+1/x)^3=27=>x^3+1/x^3=27-3×3=27-9=18ans

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@ryemiranda6800]

Nice Keep it up man 👍

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@yalchingedikgedik8007]

Thats very nice. Thanks PreMath Thanks Sir .

[@PreMath]

You are most welcome Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@lavanya.s123]

Wow ! I like your explanation very easy to understand

[@PreMath]

Thanks for liking

[@MPhani-cl9rw]

Great sir !

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@bigm383]

Thanks Professor!❤

[@PreMath]

My pleasure! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@unknownidentity2846]

Very nice trick. Here is my alternative solution without solving for x: x² − 3x + 1 = 0 x² = 3x − 1 x³ = x²x = (3x − 1)x = 3x² − x = 3(3x − 1) − x = 9x − 3 − x = 8x − 3 x³ + 1/x³ = (8x − 3) + 1/(8x − 3) = [(8x − 3)² + 1]/(8x − 3) = (64x² − 48x + 9 + 1)/(8x − 3) = [64(3x − 1) − 48x + 10]/(8x − 3) = [192x − 64 − 48x + 10]/(8x − 3) = (144x − 54)/(8x − 3) = 18(8x − 3)/(8x − 3) = 18 Best regards from Germany.

[@alkathakur74]

Nice

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@romilsonmagalhaes6487]

That's cool.

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀

[@romilsonmagalhaes6487]

@@PreMath 👏👏

[@wackojacko3962]

Those famous identities ! Mmmmmm! The ultimate reason math is fun! 🙂

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@profjiknyolal6108]

Help me solve for x. : Log (x+23) to base 3 is equal to log(72-8x) to base 2

[@khalidayubi01]

👍

[@PreMath]

Thanks for your feedback! Cheers! 😀

[@giuseppemalaguti435]

18

[@alkathakur74]

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