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Nairaland Forum / Science/Technology / Programming / How Do You Solve (x^3)+x-16=0 ? (779 Views)
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How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 1:45pm On Mar 24, 2023 |
How do you solve (x^3)+x-16=0 ? I was solving an exponential equation and it came to this and I am stuck. Calculators can produce the answers but I want to get the working. Its been getting me worried for the past 5 days now. Original Question (2^x)+2^(3x)=16 |
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 1:59pm On Mar 24, 2023 |
Post the original question 1 Like |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 2:04pm On Mar 24, 2023 |
meum:Done. |
Re: How Do You Solve (x^3)+x-16=0 ? by airsaylongcome: 2:16pm On Mar 24, 2023 |
It's been a long time I did all this algebra gymnastics. Why aren't you doing something like 2^x+2^(3x)=2^4? And simplify as they have similar base? Na 20+ years ago I do these kind things last |
Re: How Do You Solve (x^3)+x-16=0 ? by NLegendforte: 2:26pm On Mar 24, 2023 |
X na 1 |
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 2:43pm On Mar 24, 2023 |
Is the solution from the calculator 1.2556? Let me know so I can share the step by step working |
Re: How Do You Solve (x^3)+x-16=0 ? by Sleekcode: 3:16pm On Mar 24, 2023 |
meum: If you're confident of your answer you won't be posting this. Unless you have no idea what you're solving. |
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 3:22pm On Mar 24, 2023 |
Sleekcode:Why una like fight like dis for dis forum & the country sef? Oga carry pen & paper. Question dey dia. Solve your own! E no hard. Allow make d poster answer me. No be today I begin solve maths problem for this forum. |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 3:33pm On Mar 24, 2023 |
meum:Yes. If I had used casio natural display maybe I would have analysed the answer in surd form and try to work it back . |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 3:36pm On Mar 24, 2023 |
airsaylongcome:I tried this but I couldn't get farther than that so I decided to factorize. When I factorized the indices and substituted an arbitrary letter 'x' for 2x, the cubic equation became a problem too |
Re: How Do You Solve (x^3)+x-16=0 ? by platymus: 3:38pm On Mar 24, 2023 |
That's the answer I got. 1 Like
|
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 3:38pm On Mar 24, 2023 |
BenedictAbajue:Okay. I will send in the step by step solution soon. Let me make it visible enough.😂 (2^x) + 2^(3x) = 16 ie. 2^x + 2^x*3 = 16 ……eqn 1 Now let 2^x = y ….. eqn 2 Eqn 1 becomes y + y^3 = 16 rearranging this you will have: y^3 + y - 16 = 0 …….eqn 3 The above, equation 2 is in the form y^3 + py+ q = 0 ……eqn 4 Applying Cardano’s formula below y=(3√−q/2+√q^2/4+p^3/27) + (3√−q/2−√q^2/4+p^3/27). Comparing eqns 3 & 4 then substituting the values for p & q you’ll have: y = 2.387 (plug in the values yourself) Now from eqn 2, 2^x = y This implies that 2^x = 2.387 Taking log of both sides, you will have log 2^x = log 2.387 This implies that: xlog2 = log2.387 x = log2.387 / log2 Therefore x = 1.2556 👍 Ask questions where you don’t understand. Note the 3√ in cardona’s formula covers the entire values within each bracket() & it means cube root not 3*√ By log I imply log to base ten(10) of both sides 2 Likes |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 4:05pm On Mar 24, 2023 |
meum:Alright |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 4:08pm On Mar 24, 2023 |
platymus:You can't add up their index like that unless it was multiplication instead of addition that was between them |
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 4:32pm On Mar 24, 2023 |
platymus:Nah. Maths rule was broken. |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 5:04pm On Mar 24, 2023 |
meum:This is the first time I an hearing of Cardano's formula. So the formula works for all equations in that form. I was hoping to see a direct solving of the cubic equation itself. What if the question was something like this: (2^x)+3^(3x)=16 |
Re: How Do You Solve (x^3)+x-16=0 ? by meum: 5:20pm On Mar 24, 2023 |
BenedictAbajue: The Cardano's formula (named after Girolamo Cardano 1501-1576), which is similar to the perfect-square method to quadratic equations, is a standard way to find a real root of a cubic equation. If the question were written as above then it will be mathematically incorrect😂 |
Re: How Do You Solve (x^3)+x-16=0 ? by LikeAking: 6:44pm On Mar 24, 2023 |
meum: Nice! |
Re: How Do You Solve (x^3)+x-16=0 ? by chukwuebuka65(m): 6:46pm On Mar 24, 2023 |
Re: How Do You Solve (x^3)+x-16=0 ? by Deicide: 7:48pm On Mar 24, 2023 |
Since this is a programming section, you have to solve the the programming way using something like numerical analysis.. You could start from 0 to maybe like a million and input them as value of x to see if it equat zero then break. Lol computers would do this very fast. You could also try negative numbers too. Answer can also be decimal you could also check for that too. |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 8:52am On Mar 25, 2023 |
meum:'Incorrect' like there is no answer or that the formula wont work on it. Which one? |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 8:54am On Mar 25, 2023 |
Deicide:I could do this with python but I need the solvings. |
Re: How Do You Solve (x^3)+x-16=0 ? by 2paid2Bmad: 11:44am On Mar 25, 2023 |
platymus: This was how we were taught in secondary school, so anybody screaming Cardano or Cardoso or Ethereum formula take note, doesn’t this also arrive at the same answer without stress?? |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 12:49pm On Mar 25, 2023 |
2paid2Bmad:Oya put 1 into the equation and check if you are correct na |
Re: How Do You Solve (x^3)+x-16=0 ? by studyless123: 1:50pm On Mar 26, 2023 |
BenedictAbajue: 2^x + 2^3x = 16 = 2^x + 2^x+2x = 16 = 2^x (1+2^2x) = 16 = 1 + 2^(2x) = 16 / 2^x = 1 + 2^(2x) = 2^4 / 2^x = 1 + 2^(2x) = 2^(4-x) = 2^(2x) = 2^(4-x) - 1 = 2x = log2(2^(4-x) - 1) = 2x = log2(2^(4-x)) + log2(1 - 1/2^(4-x)) = 2x = (4-x)log2(2) + log2(2^(4-x) - 1) = x = (4 + log2(2^(4-x) - 1)) / 3 |
Re: How Do You Solve (x^3)+x-16=0 ? by BenedictAbajue(m): 6:41pm On Mar 26, 2023 |
studyless123:From this point, it went all wrong. |
Re: How Do You Solve (x^3)+x-16=0 ? by captainbangz: 9:33am On Mar 27, 2023 |
(x^3)+x-16=0. (x^3)+(0x^2)+x-16=0. (((x+0)x+1)x-16). Use trial method (random consecutive numbers in place of "x"), when the trinomial equals zero, that is one solution or root of the equation. You then do polynomial division to get the remainder which is a quadratic equation and solve for the remaining roots. |
Re: How Do You Solve (x^3)+x-16=0 ? by tope6217: 10:57pm On Mar 27, 2023 |
platymus: Wrong answer |
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