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 the following:
`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`
Solve the following equation for x:
`7^(2x+3)=1`
Solve the following equation for x:
`2^(5x+3)=8^(x+3)`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
Write \[\left( 625 \right)^{- 1/4}\] in decimal form.
Which of the following is (are) not equal to \[\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}\] ?
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
Find:-
`32^(2/5)`
