Question

given, a +b+c=1, ab+bc+ca=1/3,then,a:b:c=?

Answer 1

★ LINEAR REDUCTION ★

a + b + c = 1

FOR GENERALITY ;
a = b = c = 1/3

AND IT SATISFIES THE GIVEN DATA THAT
ab + bc + ca = 1/3

Aslike -
1/9 + 1/9 + 1/9 = 1/3

HENCE ;

a : b : c = 1/3 : 1/3 : 1/3 = 1 : 1 : 1


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Answer 2

Hey here is the solution....

(a+b+c)²=(1)²

or,a²+b²+c²+2(ab+bc+ca) =1

or, a²+b²+c²=1-2×1/3

or, a²+b²+c²= 1/3

or, a²+b²+c² = ab + bc+ca

or, 2a²+2b²+2c²=2ab+2bc+2ca

or,(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ca+a²)=0

or, (a-b)=0 or, (b-c) or, (c-a)=0

or, a=b or, b=c or, c=a

Therefore, a:b:c=1:1:1

Hope it helps you

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