Let a, b, c be the three distinct positive real numbers such that 
and 
. Then 6a + 5bc is equal to______.
Text Solution
Verified by Experts8
(8)
Given equation: (2a) ln(a) = (bc) ln(b)
ln(a)-(ln(2a))= ln(b)-ln(bc)
ln(a)-(ln(b)+ln(a))= ln(b)-(ln(b)+ln(c))
let ln(a)= x, ln(b)= y, ln(c)= 2, x 
y 
z
x(ln(b)+x)= y(y + z)
x ln(b)= y 2 - x 2 + yz........(i)
Similarly, from second equation
ln(b).ln(b)=ln(c)-ln(a)
......(ii)
Substitute eq(ii) in eq(i),
We get,
Now x = -y, y =-z and x = z
Hence this is the required answer.
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