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`
If ax = by = cz and b2 = ac, show that `y=(2zx)/(z+x)`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
Write \[\left( 625 \right)^{- 1/4}\] in decimal form.
The value of x − yx-y when x = 2 and y = −2 is
If (23)2 = 4x, then 3x =
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
The value of \[\left\{ \left( 23 + 2^2 \right)^{2/3} + (140 - 19 )^{1/2} \right\}^2 ,\] is
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
