Question

pls send the solution fast pls

Answer 1

Answer:

Option A

Step-by-step explanation:

Given :-

a+b+c = 0

To find:-

Find the value of [{(a+b)/-c}+{(c+a)/-b}+{(b+c)/-a}]/3 ?

Solution:-

Given that :

a+b+c = 0

=> a+b = - c --------(1)

or

=> b+c = -a ---------(2)

or

=> c+a = -b ----------(3)

Now,

The value of [{(a+b)/-c}+{(c+a)/-b}+{(b+c)/-a}]/3

=> [{-(a+b)/c}+{-(c+a)/b}+{-(b+c)/a}]/3

=> [[{-(a+b)ab}+{-(c+a)ca}+{-(b+c)bc}]/(abc)]/3

=> [{-(a²b+ab²)}+{-(c²a+ca²)}+{-(b²c+bc²)}]/(3abc)

=> [-a²b-ab²-ac²-a²c-b²c-bc²]/(3abc)

=>[(-a²b-a²c)+(-b²a-b²c)+(-c²a-c²b)]/(3abc)

=> [-a²(b+c)-b²(a+c)-c²(a+b)]/(3abc)

From (1) , (2) and (3)

=> [-a²(-a) -b²(-b) -c²(-c)]/(3abc)

=> (a³+b³+c³)/(3abc)

Answer:-

The value of [{(a+b)/-c}+{(c+a)/-b}+{(b+c)/-a}]/3 for the given problem is (a³+b³+c³)/(3abc)

Note :-

We get (a³+b³+c³)/(3abc)

We know that

If a+b+c = 0 then a³+b³+c³ = 3abc

Then above expression becomes

=> 3abc/3abc

=> 1

Used formulae:-

• If a+b+c = 0 then a³+b³+c³ = 3abc