Advertisements
Advertisements
प्रश्न
Show that:
`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`
Advertisements
उत्तर
`(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1`
LHS = `(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)`
`=(a^(x+1-y-1))^(x+y)(a^(y+2-z-2))^(y+z)(a^(z+3-x-3))^(z+x)`
`=(a^(x-y))^(x+y)(a^(y-z))^(y+z)(a^(z-x))^(z+x)`
`=(a^((x-y)(x+y)))(a^((y-z)(y+z)))(a^((z-x)(z+x)))`
`=(a^(x^2-y^2))(a^(y^2-z^2))(a^(z^2-x^2))`
`=a^(x^2-y^2+y^2-z^2+z^2-x^2)`
`=a^0`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Solve the following equation for x:
`7^(2x+3)=1`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Simplify:
`(0.001)^(1/3)`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
Which one of the following is not equal to \[\left( \frac{100}{9} \right)^{- 3/2}\]?
If 102y = 25, then 10-y equals
If x is a positive real number and x2 = 2, then x3 =
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
Find:-
`125^(1/3)`
