Let ⁻¹ x+ ⁻¹ y+ ⁻¹ z= 3 2 for 0 x, y, z 1 . What is the value of x¹⁰⁰⁰+y¹⁰⁰¹+z¹⁰⁰² ?

Step-by-step solution

⁻¹(x)+ ⁻¹(y)+ ⁻¹(z)= 3 2 = 2 + 2 + 2 aligned & ⁻¹(x)= 2 , ⁻¹(y)= 2 , ⁻¹(z)= 2 & x=y=z=1 [ as ⁻¹(1)= 2 ] & So, x¹⁰⁰⁰+y¹⁰⁰¹+z¹⁰⁰² & 1+1+1=3 aligned