Question

If ab+bc+ca=0 then find the value of 1/a²-bc+1/b²-ca+1/c²-ab

Answer 1

Answer:

Step-by-step explanation:

ab+bc+ca=0

bc=−ca−ab

bc=−a(b+c)---eq1

like wise,

ab=−c(a+b)---eq2

& ca=−b(c+a)---eq3

=  

a  

2

−bc

1

​  

+  

b  

2

−ca

1

​  

+  

c  

2

−ab

1

​  

 

taking the value from eq1, 2&3

=  

a  

2

+a(b+c)

1

​  

+  

b  

2

+b(a+c)

1

​  

+  

c  

2

+c(a+b)

1

​  

 

=  

a(a+b+c)

1

​  

+  

b(a+b+c)

1

​  

+  

c(a+b+c)

1

​  

 

=  

abc(a+b+c)

ab+bc+ca

​  

 

As ab+bc+ca=0

So, =0