Solving for Equality with Positive a and b

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SUMMARY

The discussion centers on proving the mathematical equality involving positive variables a and b, specifically: (a² + a^(4/3)b^(2/3))^(1/2) + (b² + a^(2/3)b^(4/3))^(1/2) = (a^(2/3) + b^(2/3))^(3/2). Participants emphasize the importance of algebraic manipulation and the application of the Cauchy-Schwarz inequality to establish the proof. The equality holds under the condition that both a and b are positive and non-zero.

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  • Understanding of algebraic manipulation
  • Familiarity with the Cauchy-Schwarz inequality
  • Knowledge of exponent rules and properties
  • Basic concepts of mathematical proofs
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  • Study the Cauchy-Schwarz inequality and its applications in proofs
  • Explore algebraic identities and their proofs
  • Learn about manipulating expressions with exponents
  • Practice solving inequalities involving positive variables
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Mathematics students, educators, and anyone interested in algebraic proofs and inequalities involving positive variables.

tatoo5ma
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hello everyone,

I have a problem, if anyone can get me started. Thanks

I have to show this equality knowing that a and b are positive and they do not euqal 0:

[tex](a^{2}+a^{\frac{4}{3}}b^{\frac{2}{3}})^{\frac{1}{2}} + (b^{2}+a^{\frac{2}{3}}b^{\frac{4}{3}})^{\frac{1}{2}} =(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}[/tex]

now I have no idea where to start!
 
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