If a, b and c are non-zero real numbers and if the system of equations (a - 1)x=y+z, (b - 1)y=z+x and (c - 1)z=x+y have a non-trivial solution, then (3/2 a)+(3/2 b)+(3/2 c) is equal to

Question

If a, b and c are non-zero real numbers and if the system of equations (a - 1)x=y+z, (b - 1)y=z+x and (c - 1)z=x+y have a non-trivial solution, then (3/2 a)+(3/2 b)+(3/2 c) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

System of equations can be written as (a - 1)x-y-z=0 x-(b - 1)y+z=0 x+y-(c - 1)z=0 Using Cramer's rule, for non-trivial solution Δ =0 | (a - 1) -1 -1 1 -(b - 1) 1 1 1 -(c - 1) |=0 ⇒ (a - 1)[(b - 1) (c - 1) - 1]-(- 1)[- (c - 1) - 1]-1[1 + b - 1]=0 ⇒ (a - 1)[b c - b - c]-c-b=0 ⇒ abc-ab-ac-bc+b+c-c-b=0 ⇒ ab+bc+ca=abc⇒ ((1/a) + (1/b) + (1/c))=1

Q. If a,b and c are non-zero real numbers and if the system of equations (a−1)x=y+z,(b−1)y=z+x and (c−1)z=x+y have a non-trivial solution, then 2a3​+2b3​+2c3​ is equal to

Q. If $a, b$ and $c$ are non-zero real numbers and if the system of equations $(a - 1) x = y + z, (b - 1) y = z + x$ and $(c - 1) z = x + y$ have a non-trivial solution, then $\frac{3}{2 a} + \frac{3}{2 b} + \frac{3}{2 c}$ is equal to