Advertisements
Advertisements
Question
If `a = 2 + sqrt(3)`, then find the value of `a - 1/a`.
Advertisements
Solution
Given that `a = 2 + sqrt(3)`,
∴ We have `1/a = 1/(2 + sqrt(3))`
⇒ `1/a = 1/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3))` ...[Using (a – b)(a + b) = a2 – b2]
⇒ `1/a = (2 - sqrt(3))/(4 - 3)`
⇒ `1/a = 2 - sqrt(3)`
Now ` a - 1/a = 2 + sqrt(3) - (2 - sqrt(3))`
⇒ `a - 1/a = 2sqrt(3)`
APPEARS IN
RELATED QUESTIONS
Simplify:-
`2^(2/3). 2^(1/5)`
Prove that:
`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`
Simplify:
`(16^(-1/5))^(5/2)`
If 3x = 5y = (75)z, show that `z=(xy)/(2x+y)`
State the product law of exponents.
Simplify \[\left[ \left\{ \left( 625 \right)^{- 1/2} \right\}^{- 1/4} \right]^2\]
The seventh root of x divided by the eighth root of x is
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
Simplify:
`7^(1/2) . 8^(1/2)`
