Advertisements
Advertisements
प्रश्न
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
Advertisements
उत्तर
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
LHS = `(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)`
`=(3^(a-b))^(a+b)(3^(b-c))^(b+c)(3^(c-a))^(c+a)`
`=(3^((a-b)(a+b)))(3^((b-c)(b+c)))(3^((c-a)(c+a)))`
`=(3^(a^2-b^2))(3^(b^2-c^2))(3^(c^2-a^2))`
`=3^(a^2-b^2+b^2-c^2+c^2-a^2)`
`=3^0`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Simplify the following
`((4xx10^7)(6xx10^-5))/(8xx10^4)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Prove that:
`(64/125)^(-2/3)+1/(256/625)^(1/4)+(sqrt25/root3 64)=65/16`
Prove that:
`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
The value of \[\left\{ 2 - 3 (2 - 3 )^3 \right\}^3\] is
`(2/3)^x (3/2)^(2x)=81/16 `then x =
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If 102y = 25, then 10-y equals
If (16)2x+3 =(64)x+3, then 42x-2 =
If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then
