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Given that x^3a = y^2b = z^4c = xyz, then 3ab + 4bc + 6ca = ?

Given that x^3a = y^2b = z^4c = xyz,


then 3ab + 4bc + 6ca = ?

Grade:8

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
420 Points
13 years ago

Dear Vignesh

given

X3a = Y2b = Z4c = XYZ

writing Y and Z in terms of X using above relation

Y=X3a/2b, and Z=X3a/4c

now XYZ = X*X3a/2b*X3a/4c

            = X1+(3a/2b)+3a/4c

       XYZ    = X(4bc+6ac+3ab)/4bc.........(1)

from given relation XYZ= X3a........(2)

from (1) and (2)

X3a=X(4bc+6ac+3ab)/4bc

3a=(4bc+6ac+3ab)/4bc

hence 3ab + 4bc + 6ca = 12abc  Answer

 

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

 

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