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
Find the value of x in the following:
`5^(2x+3)=1`
If `x=2^(1/3)+2^(2/3),` Show that x3 - 6x = 6
If a and b are different positive primes such that
`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.
The seventh root of x divided by the eighth root of x is
If a, b, c are positive real numbers, then \[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a}\] is equal to
`(2/3)^x (3/2)^(2x)=81/16 `then x =
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
