A Method for Radical Equation: A Surprising Twist | Chinese Math Olympiad

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How to solve this equation from the Mathematical Olympiad? This algebra video presents step-by-step the basic algebraic techniques and tricks to solve this radical equation quickly and easily. For another Math Olympiad problem: • Solve Quartic Equation...
Discover a clever and unique approach to solving radical equations with multiple square roots. In this video, we unveil an ingenious method that simplifies the process, allowing you to crack the equation's code with ease. Say goodbye to complex algebraic steps and embrace a smarter way to solve equations. Watch now and unlock the power of this surprising equation-solving technique.
For more questions, tips and tricks like this, please visit Dr Wang's Channel: / @drwangusa
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Опубликовано:

16 окт 2024

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Комментарии : 11

@DrWangUSA 10 месяцев назад

Recommended Videos: Math Olympiad | Quartic Equation: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CLb7XVXGUg0.html Special Tricks to Diophantine Equation | Math Olympiad : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5bAiyzCerRs.html The Art of Diophantine Problem-Solving | Math Olympiad: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2zUGhkVHVMw.html Prime Number Equation Chinese Math Olympiad : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-JelwvsR9A78.html Exponential Diophantine Equation | Math Olympiad : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-AoQaGriEZUo.html

@ranshen1486 10 месяцев назад

Same idea in slightly different notations: Let S=sum of a, b, c & d and let Q=sum of their squares. (Note that Q=10x - 16 as in the video). Then 2+Q/2 = S ≤ 4√(Q/4) where the "=" sign is shown in the vidoe but the "≤" sign comes from the QM-AM inequality. This solves to (√Q-2)² ≤ 0 , i.e., Q=4. In terms of x, that is Q = 10x -16 =4 and thus x = 2. Essentially, this approach completes one square in terms of Q, compared with completing 4 squares in terms of a, b, c, and d.

@DrWangUSA 10 месяцев назад

Nice method and thanks for sharing!

@에스피-h8t 10 месяцев назад

Solution by insight 1+1+1+1=5×2-6 x=2

@DrWangUSA 10 месяцев назад

Nice try!

@SrisailamNavuluri 9 месяцев назад

x-1=(x-2)+1,2x-3=2(x-2)+1,3x-5=3(x-2)+1,4x-7=4(x-2)+1 5x-6=5(x-2)+4 Here when x=2,lhs=√1+√1+√1/√1=4=rhs So x=2

@DrWangUSA 9 месяцев назад

Thanks for sharing

@honestadministrator 10 месяцев назад

a =√(x - 1), b =√(2 x -3), c = √(3 x -5) d = √ (4 x - 7) Hereby a^2 + b^2 + c^2 + d^2 = 10 x - 16 2( a + b + c + d) = a^2 + b^2 + c^2 + d^2 + 4 (a - 1)^2 + (b - 1)^2 + (c - 1)^2 + (d - 1)^2 = 0 Hereby x - 1 = 2 x - 3 = 3 x - 5 = 4 x - 7 = 1 all 4 equations give same solution x = 2

@DrWangUSA 9 месяцев назад

Thanks for sharing