Advertisements
Advertisements
प्रश्न
Prove that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Advertisements
उत्तर
Consider the left hand side:
`1/(1+x^(a-b))+1/(1+x^(b-a))`
`=1/(1+x^a/x^b)+1/(1+x^b/x^a)`
`=1/((x^b+x^a)/x^b)+1/((x^a+x^b)/x^a)`
`=x^b/(x^b+x^a)+x^a/(x^a+x^b)`
`=(x^b+x^a)/(x^a+x^b)`
= 1
Therefore left hand side is equal to the right hand side. Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that:
`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
State the quotient law of exponents.
The square root of 64 divided by the cube root of 64 is
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
Find:-
`32^(1/5)`
