SOLUTION: If a+b=6/3 and ab=4/3 ,then find the value of a/b+b/a+2[1/a +1/b]

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Question 1077614: If a+b=6/3 and ab=4/3 ,then find the value of a/b+b/a+2[1/a +1/b]
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Fb%2Bb%2Fa%2B2%281%2Fa%2B1%2Fb%29

%28a%5E2%2Bb%5E2%29%2F%28ab%29%2B2%28b%2Ba%29%2F%28ab%29

%28a%5E2%2Bb%5E2%2B2b%2B2a%29%2F%28ab%29

Substitute for ab=4%2F3.
%28a%5E2%2Bb%5E2%2B2a%2B2b%29%2F%284%2F3%29

3%28a%5E2%2Bb%5E2%2B2a%2B2b%29%2F4

%283%2F4%29%28a%5E2%2B2a%2B2b%2Bb%5E2%29

%283%2F4%29%28a%2Bb%29%28a%2Bb%29-------THIS STEP IS MISTAKE. THE REST IS WRONG.


-----------------------------------------------------------------
Substitute for a%2Bb=6%2F3.
%283%2F4%29%286%2F3%29%286%2F3%29

%283%2F4%29%282%2A2%29

cross%283%29-----Not correct

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
If a+b=6/3 and ab=4/3 ,then find the value of a/b+b/a+2[1/a +1/b]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Separate  a/b+b/a+2[1/a +1/b]  in two parts:

a%2Fb+%2B+b%2Fa  and  2%281%2Fa%2B1%2Fb%29 and evaluate each part SEPARATELY.

Also notice that a + b = 6%2F3 = 2.



1.  a%2Fb+%2B+b%2Fa = a%5E2%2F%28ab%29+%2B+b%5E2%2F%28ab%29 = %28a%5E2+%2B+b%5E2%29%2F%28ab%29 = %28%28a%5E2+%2B+2ab+%2B+b%5E2%29+-+2ab%29%2F%28ab%29 = %28a%2Bb%29%5E2%2F%28ab%29 - 2 = 2%5E2%2F%28ab%29 - 2 = 4%2F%28ab%29 - 2 = 4%2F%28%284%2F3%29%29 - 2 = 3 - 2 = 1.


    Everywhere where it is possible, I replaced (a+b) by 2 and ab by (4/3).


2.  2%2A%281%2Fa+%2B+1%2Fb%29 = 2%2A%28b%2F%28ab%29+%2B+a%2F%28ab%29%29 = 2%2A%28%28a%2Bb%29%2F%28ab%29%29 = 2%2A%282%2F%28%284%2F3%29%29%29 = 3.


    Again, everywhere where it is possible, I replaced (a+b) by 2 and ab by (4/3).



3.  The last step is to combine what you get in n.1 and in n.2. Then you have


    a/b+b/a+2[1/a +1/b]  = 1 + 3 = 4.


Answer. a/b+b/a+2[1/a +1/b] = 4.


Do not spend your time reading "the solution" by "josgarithmetic".

IT IS WRONG.

Simply IGNORE it.


This person has no any understanding/ (has no any knowledge) how to solve such problems, but always tends to be before me.