WMC 2018 Pursuit - Pack 2, D2

Algebra Level 3

If ( a + b ) : ( b + c ) : ( a + c ) = 1 : 3 : 7 (a+b):(b+c):(a+c)=1:3:7 and a + b + c = 11 a+b+c=-11 , find a b c abc .

WMC Pursuit Questions


The answer is 135.0.

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1 solution

X X
Oct 5, 2018

( a + b ) : ( b + c ) : ( c + a ) : 2 ( a + b + c ) = 1 : 3 : 7 : ( 1 + 3 + 7 ) = ( 2 ) : ( 6 ) : ( 14 ) : ( 22 ) (a+b):(b+c):(c+a):2(a+b+c)=1:3:7:(1+3+7)=(-2):(-6):(-14):(-22)

Solve for a + b = 2 , b + c = 6 , c + a = 14 a+b=-2,b+c=-6, c+a=-14 and get a = 5 , b = 3 , c = 9 , a b c = 135 a=-5,b=3,c=-9,abc=135

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