If x b-c = y c-a = z a-b , then the value of x^ b+c y^ c+a z^ a+b is

Step-by-step solution

Given, x b-c = y c-a = z a-b =k (say) (i) x=e^ k(b-c) , y=e^ k(c-a) , z=e^ k(a-b) Now, x^ b+c y^ c+a z^ a+b =e^ k(b-c)(b+c) e^ k(c+a)(c-a) e^ k(a+b)(a-b) aligned &=e^ k (b²-c² ) e^ k (c²-a² ) e^ k (a²-b² ) &=e^ k (b²-c²+c²-a²+a²-b² ) =e^ k 0 =1 aligned