Advertisements
Advertisements
प्रश्न
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Advertisements
उत्तर
`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^b+x^a)`
= 1
APPEARS IN
संबंधित प्रश्न
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
Show that:
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Show that:
`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
Find the value of x in the following:
`(sqrt(3/5))^(x+1)=125/27`
State the quotient law of exponents.
If 3x-1 = 9 and 4y+2 = 64, what is the value of \[\frac{x}{y}\] ?
If 9x+2 = 240 + 9x, then x =
If 10x = 64, what is the value of \[{10}^\frac{x}{2} + 1 ?\]
