Advertisements
Advertisements
प्रश्न
Show that:
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
उत्तर
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
LHS = `(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))`
`=(x)^(1/(a-b)xx1/(a-c))(x)^(1/(b-c)xx1/(b-a))(x)^(1/(c-a)xx1/(c-b))`
`=(x)^(1/(a-b)xx1/(a-c)+1/(b-c)xx1/(b-a)+1/(c-a)xx1/(c-b))`
`=(x)^(((b-c)-(a-c)+(a-b))/((a-b)(a-c)(b-c)))`
`=x^0`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Find:-
`64^(1/2)`
Simplify the following
`(2x^-2y^3)^3`
Simplify:
`root5((32)^-3)`
Simplify:
`(sqrt2/5)^8div(sqrt2/5)^13`
Show that:
`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`
If 2x = 3y = 12z, show that `1/z=1/y+2/x`
State the power law of exponents.
If \[4x - 4 x^{- 1} = 24,\] then (2x)x equals
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
