Solve and Check x^21 + x^14 = 36 for real solutions | Olympiad Mathematics | Math Olympiad Training

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Solve and Check x^21 + x^14 = 36 for real solutions | Olympiad Mathematics | Math Olympiad Training

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Your vdos make my mood fresh
Thankyou ❤️dear ❤️

rishudubey
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And now let's recall, Power Rule, Substitution, Solve Cubic Equation by grouping and factoring, Replace, Manipulation, Difference of two squares identity, Replace, Factor out, Distribute, Separate, Quadratic Formula, Discriminate Rule, Take root, Check solution, Basic Rule of roots, Power Rule. WOW!

prbmax
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Answer 1.17 or 3^1/7
let n=x^7
then n^3 + n^2 = 36
n = 3 as
3^3 + 3^2 = 36
hence 3 =x^7
3^1/7=x Answer
1.17= x Answer

devondevon
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Very good! I found it easy, since I know that 36 is 3^3 + 3^2, it became easy to find out that x is 3^(1/7).

matematicafacilcomprof.jua
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why don't you use synthetic division?

dandeleanu
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Excellent video, very well explained. I just want to ask how did you get: -3a^2 +4a^2 ?

sahiljain
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Very well explained👍
Thanks for sharing😊

HappyFamilyOnline
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Let y=x^7, we have y^3+y^2-36=0, ....how to proceed?

misterenter-izrz
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What is the solution if 7 root 3 is solved ? i really want to know the number. Will it be a endless or will it have a end?

guidosillaste
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I have an easier approach though...

I used a combination of 3 methods

1.) Rational Zero Theorem
2.) Factor/Remainder Theorem
3.) Synthetic Division
I listed down all the possible zeroes with the RZT (Rational Zero Theorem)
and then with the Factor/Remainder Theorem, I substituted each value, but when I substituted a= 3 in the original equation, it resulted to 0. Thus a= 3 is the answer. To double check for other possible solutions, I proceeded with Synthetic Division and divided a³+a²-36 by a-3

Thus resulting in a²+4a+12 and followed the same procedure as stated in the video.

alster
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If the points A(5, 8), B(8, 0), C(0, 4), D(0, 5) and O(0, 0) are plotted on graph paper, then the point on x axis are

a) A and C

b) C and D

c) only B

d) B and O


PLEASE HELP ME OUT!

vivekscreation
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ChatGPT couldn't solve this equation.

NANICU