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If a + b = 7 and a^3 + b^3 = 42 + ab, what is the value of the sum 1/a + 1/b? Express you answer as a common fraction. 

 May 17, 2021
 #1
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1/a + 1/b = 4/17.

 May 17, 2021
 #2
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(a + b) =  7       cube both sides

 

a^3  +  3a^2b + 3ab^2  + b^3    =  343

 

a^3 + b^3   + 3ab ( a + b)    =  343

 

42  + ab  +  3ab ( 7)   =  343

 

42   +  22ab  =  343

 

22ab  =  301

 

ab  = 301 / 22

 

And

 

1/a  + 1/b =    [ a + b ]  / ab  =     7 / ( 301/22)   =  22 * 7  / 301   =  154 / 301  = 22  / 43

 

cool cool cool

 May 17, 2021

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