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If a + b = 7 and a^3 + b^3 = 44, what is the value of the sum 1/a + 1/b? Express your answer as a common fraction.

 Aug 1, 2022
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a + b =  7                square both sides

 

a^2  + 2ab +b^2  = 49

 

a^2 + b^2  = 49  - 2ab

 

And

 

a^3 + b^3  =  44

 

(a + b) ( a^2  - ab + b^2)  = 44

 

(a + b)  ( a^2 + b^2  - ab)  = 44

 

(7) ( 49 - 2ab -ab)  =  44

 

49 - 3ab  =  44/7

 

49 - 44/7  = 3ab

 

299/7  =  3ab

 

299 / 21  =  ab

 

Note that    1/a + 1/b =  (a + b) /  ab   =    7 / ( 299/21)  = 147 / 299

 

 

cool cool cool

 Aug 1, 2022

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