य‌द‌ि `(x-a^(2))/(b+c)+(x-b^(2))/(c+a)+(x-c^(2))/(a+b)=4(a+b+c)`, then `x` ‌ किसके बराबर है ?

Options

A. `(a+b+c)^(2)`
B. `a^(2)+b^(2)+c^(2)`
C. `ab+bc+ca`
D. `a^(2)+b^(2)+c^(2)-ab-bc-ca`

Answer

A

Explanation

`(x-a^(2))/(b+c)=(x-b^(2))/(c+a)+(x-c^(2))/(a+b)`
`=4(a+b+c)`
assume `a=1, b=0, c=1`
Make sure thre will no `(0/0)` form
`: (x-1)/(1+0)+(x-0)/(1+1)+(x-1)/(1+0)=4`
`implies x-1+x/2+x-1=4xx2`
`x+x/2+x=8+2`
`(5x)/2=10`
`x=4`
Now put values in options take option.
`(a)(a+b+c)^(2)-(1+0+1)^(2)=4`