If the equations a(y+z)=x, b(z+x)=y and c(x+y)=z, where a -1, b -1, c -1, admit of nontrivial solutions then (1+a)^ -1 +(1+b)^ -1 +(1+c)^ -1 is

JEE Advanced Mathematics question

If the equations , and , where , , , admit of nontrivial solutions then

(1++(1++(1+

Answer: (A)

Add to both sides of the first equation (and similarly for the others). With :

aS=(1+a)x, bS=(1+b)y, cS=(1+c)z .

If , then gives (since ), and likewise . That is the trivial solution. So for a nontrivial solution , and

x=S, y={

Create a free account to read the complete working (7 steps), and practise questions like this in a timed test.

Question ID VK-108282