Advertisements
Advertisements
Question
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
Options
\[2\sqrt{5}\]
4
2
\[\sqrt{5}\]
Solution
Given that. `x=sqrt5 +2 ` Hence `1/x`is given as
`1/x = 1/(sqrt5+2)`.We need to find `x - 1/x`
We know that rationalization factor for `sqrt5+2` is`sqrt5-2`. We will multiply numerator and denominator of the given expression\`1/(sqrt5 +2)` by`sqrt5 - 2`, to get
`1/x = 1/(sqrt5+2 ) xx (sqrt5 - 2)/(sqrt5 -2)`
` = (sqrt 5-2)/((sqrt5)^2 - (2)^2 )`
`=(sqrt5 -2)/(5-4)`
` = sqrt5 - 2`
Therefore,
`x - 1/x=sqrt5 +2 -(sqrt5 - 2)`
`= sqrt5 +2 - sqrt5 +2`
` = 2+2`
` = 4`
APPEARS IN
RELATED QUESTIONS
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(3 - sqrt5)/(3 + 2sqrt5)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`(sqrt(10) - sqrt(5))/2`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
