Question

the value of the expression (x+y+z)/(x^-1y^-1+y^-1z^-1+z^-1x-1)​




ans this 99 points​

Answer 1

xyz=1. Let x=a/b,y=b/c,z=c/a

1+x+y^(-1)=1+a/b+c/b=(a+b+c)/b

1+y+z^(-1)=1+b/c+a/c=a+b+c/c

1+z+x^(-1)=1+c/a+b/a=a+b+c/a

(1+x+y^(-1))^(-1)+(1+y+z^(-1))^(-1)+ (1+z+x^(-1))^(-1)=b/a+b+c + c/a+b+c + a/a+b+c=a+b+c/a+b+c=1(answer)

Answer 2

Given expression is =>

(x+y+z)/{(x^1)(y^-1)+(y^-1)(z^-1)+(z^-1)(x-1)}

So on simplifying we get =>

=>(x+y+z)/{(1/x)( 1/y) +(1/y)(1/z)+(1/z)1/x)}

=>(x+y+z)/(1/xy + 1/yz + 1/xz)

=>(x+y+z)/{(x+y+z)/xyz}

=>xyz

Hence the value of the expression (x+y+z)/(x^-1y^-1+y^-1z^-1+z^-1x-1) will be xyz.

Remember

1)Something to the power minus 1 means it would be inverted.

example =>

x^-1 = 1/x

where x is variable but not equal to 0.

2)While solving such an equation always remember that to carefully first look at the equation and then decide how to solve it taking a suitable way to solve it quick.