Question

Please Answer the question. I want to do my maths assignment​

Answer 1

Answer:

Given data:

xyz = 1

To prove: [1+x+y⁻¹]⁻¹ + [1+y+z⁻¹]⁻¹ + [1+z+x⁻¹]⁻¹ = 1

Since xyz = 1, so

y = 1/zx, x = 1/yz, z = 1/xy …. (i)

Taking L.H.S

= [1+x+y⁻¹]⁻¹ + [1+y+z⁻¹]⁻¹ + [1+z+x⁻¹]⁻¹

= $\frac{1}{1+x+\frac{1}{y} }$ + $\frac{1}{1+y+\frac{1}{z} }$ + $\frac{1}{1+z+\frac{1}{x} }$

= $\frac{y}{y+xy+1 }$ + $\frac{1}{1+y+xy }$ + $\frac{1}{1+\frac{1}{xy}+\frac{1}{x}}$ ….. [from eq. (i)]

= $\frac{y}{y+xy+1 }$ + $\frac{1}{1+y+xy }$ +  $\frac{xy}{xy+1+y}$

= $\frac{y+1+xy}{y+xy+1 }$

= $\frac{1+y+xy}{1+y+xy}$

= 1

= R.H.S

Hence proved