Question

solve this
if a plus b plus c equals to zero

Answer 1

since a+b+c =0
a+b = -c
squaring both sides we get
(a+b)^2 = c^2
similarly we get this for b and c too.
Putting these in the original equation we get

$(c ^{2} \div ab) + \: (a ^{2} \div bc) \: \: + (b ^{2} \div ac)$
taking the lcm we get
$(a ^{3} + b ^{3} + c ^{3} ) \div (abc)$
also if a+b+ c = 0 then
$a ^{3} + b ^{3} + c ^{3} = \: 3abc$
hence the above expression is equal to 3.

Answer 2

since a+b+c =0
a+b = -c
squaring both sides we get
(a+b)^2 = c^2
similarly we get this for b and c too.
Putting these in the original equation we get

(c ^{2} \div ab) + \: (a ^{2} \div bc) \: \: + (b ^{2} \div ac)
taking the lcm we get
(a ^{3} + b ^{3} + c ^{3} ) \div (abc)
also if a+b+ c = 0 then
a ^{3} + b ^{3} + c ^{3} = \: 3abc
hence the above expression is equal to 3.