Question
Download Solution PDFThe value of \(\left( {{x^{\frac{2}{3}}}\, - \,{x^{\frac{1}{3}}}{y^{\frac{1}{3}}}\, + \,{y^{\frac{2}{3}}}} \right)\left( {{x^{\frac{1}{3}}} + {y^{\frac{1}{3}}}} \right) \) is _________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
(a³ + b³) = (a + b)(a² - ab + b²)
Calculations:
\(\left( {{x^{\frac{2}{3}}}\, - \,{x^{\frac{1}{3}}}{y^{\frac{1}{3}}}\, + \,{y^{\frac{2}{3}}}} \right)\left( {{x^{\frac{1}{3}}} + {y^{\frac{1}{3}}}} \right) \)
Let x1/3 be t and y1/3 be p, then
\(\left( {{x^{\frac{2}{3}}}\, - \,{x^{\frac{1}{3}}}{y^{\frac{1}{3}}}\, + \,{y^{\frac{2}{3}}}} \right)\left( {{x^{\frac{1}{3}}} + {y^{\frac{1}{3}}}} \right) \)
= (t² - tp + p²)(t + p)
= (t³ + p³)
= x + y
Hence, The Required value is x + y.
Last updated on Jun 2, 2025
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