How do we get the integer solutions ?????
–
Abhishek Mohapatra
·
3 years, 8 months ago

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it appears to be a very easy question......:) here is the probable solution....:
log[(a+b)/3]=(log a+log b)/3
=>log[(a+b)/3]=log(ab)/3
=>3log[(a+b)/3]=log(ab)
=>log[{(a+b)/3}^3]=log(ab)...........taking antilog,.......
=>[(a+b)^3]/[27]=ab
=>a^3+b^3+3ab(a+b)=27ab
=>so the integer solutions are [a=2 & b=4] ; [a=4 &b=-16] ; [a=4 & b=2].....BUT YOU SEE "b" CAN NOT TAKE NEGATIVE VALUE INSIDE LOGARITHM.....SO THE SOLUTION SHOULD BE.....[a=2 & b=4] AND [a=4 & b=2]..........................
HOPE THIS HELPS.........:))
–
Raja Metronetizen
·
3 years, 8 months ago

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@Raja Metronetizen
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how did you directly deduce the integer solns from the step:=>a^3+b^3+3ab(a+b)=27ab
–
Bhargav Das
·
3 years, 8 months ago

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@Bhargav Das
–
ha ha....!! ...i thought if anyone asks me that step by step solution.....i would crumble....!!!.....then to find the solution of a^3+b^3+3ab(a+b)=27ab i only put my graphing knowledge.........BUT EASY TO SAY YOU MAY FIND THE SOLUTION WITHOUT APPLYING YOUR BRAIN EVEN BY CLICKING HERE SIMPLY.......i only used this website to check my answer whether it is right or wrong......:-)
–
Raja Metronetizen
·
3 years, 8 months ago

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TopNewestHow do we get the integer solutions ????? – Abhishek Mohapatra · 3 years, 8 months ago

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it appears to be a very easy question......:) here is the probable solution....: log[(a+b)/3]=(log a+log b)/3

=>log[(a+b)/3]=log(a

b)/3log[(a+b)/3]=log(a=>3

b)b)...........taking antilog,....... =>[(a+b)^3]/[27]=a=>log[{(a+b)/3}^3]=log(a

bab=>a^3+b^3+3

(a+b)=27ab=>so the integer solutions are [a=2 & b=4] ; [a=4 &b=-16] ; [a=4 & b=2].....BUT YOU SEE "b" CAN NOT TAKE NEGATIVE VALUE INSIDE LOGARITHM.....SO THE SOLUTION SHOULD BE.....[a=2 & b=4] AND [a=4 & b=2].......................... HOPE THIS HELPS.........:)) – Raja Metronetizen · 3 years, 8 months ago

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– Bhargav Das · 3 years, 8 months ago

how did you directly deduce the integer solns from the step:=>a^3+b^3+3ab(a+b)=27abLog in to reply

CLICKING HERE SIMPLY.......i only used this website to check my answer whether it is right or wrong......:-) – Raja Metronetizen · 3 years, 8 months ago

ha ha....!! ...i thought if anyone asks me that step by step solution.....i would crumble....!!!.....then to find the solution of a^3+b^3+3ab(a+b)=27ab i only put my graphing knowledge.........BUT EASY TO SAY YOU MAY FIND THE SOLUTION WITHOUT APPLYING YOUR BRAIN EVEN BYLog in to reply

– Abhishek Mohapatra · 3 years, 8 months ago

How do we get the integer solutions ?????Log in to reply