Question 1077614
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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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<pre>
Separate  a/b+b/a+2[1/a +1/b]  in two parts:

{{{a/b + b/a}}}  and  {{{2(1/a+1/b)}}} and evaluate each part SEPARATELY.

Also notice that a + b = {{{6/3}}} = 2.



1.  {{{a/b + b/a}}} = {{{a^2/(ab) + b^2/(ab)}}} = {{{(a^2 + b^2)/(ab)}}} = {{{((a^2 + 2ab + b^2) - 2ab)/(ab)}}} = {{{(a+b)^2/(ab)}}} - {{{2}}} = {{{2^2/(ab)}}} - {{{2}}} = {{{4/(ab)}}} - {{{2}}} = {{{4/((4/3))}}} - {{{2}}} = 3 - 2 = 1.


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


2.  {{{2*(1/a + 1/b)}}} = {{{2*(b/(ab) + a/(ab))}}} = {{{2*((a+b)/(ab))}}} = {{{2*(2/((4/3)))}}} = 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.
</pre>


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



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


<U>IT IS WRONG</U>.


Simply <U>IGNORE it</U>.



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