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If a + b= 12 and a b= 27, find the value of a 3 +b 3 |
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Answer» +b = 12ab = 27To find:The value of a³ + b³Solution:We KNOW thata³ + b³ = (a + b)(a² +b² -ab)ALSO, (a + b)²= a² +b² + 2ab=> a²+ b² = (a + b)²- 2abNow PUTTING the value of a² + b²We GET,a³ + b³ = (a+b){ [ (a+b)²-2ab ] -ab }=> a³ + b³ = (a+b)[ (a+b)²-3ab ] Putting the valuesa³ + b³ = (12)[ (12)² - 3(27) ]=> 12 (144 - 3×27)=> 12 (144 - 81)=> 12 × 63=> 756Hence, a³ + b³ = 756 |
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