a,b,c are positive numbers such that a+b+ab= 8, b+c+bc=15 and c+a+ca = 35 What is the value of a+b+c+abc? _________
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HELLO DEAR,
GIVEN:-
a + b + ab = 8
b + a(1 + b) = 8
-------( 1 )
b + c + bc = 15
b + c(1 + b) = 15
------( 2 )
a + c + ac = 35
From----------( 1 ) &-----------( 2 )
so, b = 1 , b = -3[neglect]
because a , b , c ,are positive,
now,
from----------( 1 )
a = (8 - b)(1 + b)
a = (8 - 1)(1 + 1)
a = 7/2
from-----------( 2 )
c = (15 - b)(1 + b)
c = (15 - 1)(1 + 1)
c = 14/2
c = 7
thus, the value of "a + b + c + abc" is
7/2 + 1 + 7 + (7 * 7/2 * 1)
{(7 + 2 + 14 )/2 + 49/2}
(23/2 + 49/2)
(23 + 49)/2
72/2
36
HENCE, the value of (a + b + c + abc) = 36
I HOPE ITS HELP YOU DEAR,
THANKS
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