Advertisements
Advertisements
प्रश्न
If x = 5 - 2√6, find `x^2 + 1/x^2`
उत्तर
Given `x = 5 - 2sqrt6`
We need to find `x^2 + 1/x^2`
Since x = `5 - 2sqrt6` , we have
`1/x = 1/[ 5 - 2sqrt6]`
⇒ `1/x = 1/[ 5 - 2sqrt6 ] xx [ 5 + 2sqrt6 ]/[ 5 + 2sqrt6 ]`
⇒ `1/x = ( 5 - 2sqrt6 )/[( 5 - 2sqrt6 )( 5 + 2sqrt6 )]`
⇒ `1/x = ( 5 + 2sqrt6)/ [ 5^2 - (2sqrt6)^2 ]`
⇒ `1/x = ( 5 + 2sqrt6)/ [ 25 - 24 ]`
⇒ `1/x = ( 5 + 2sqrt6)/1`
⇒ `1/x = ( 5 + 2sqrt6)` .....(1)
Thus,`( x - 1/x ) = ( 5 - cancel(2sqrt6) ) - ( 5 + cancel(2sqrt6))` = 10
`x^2 + 1/x^2 = (x + 1/x)^2 - 2`
`x^2 + 1/x^2= (10)^2 - 2`
`x^2 + 1/x^2= 100 - 2`
`x^2 + 1/x^2 = 98`
APPEARS IN
संबंधित प्रश्न
Write the lowest rationalising factor of 5√2.
Write the lowest rationalising factor of : √24
Write the lowest rationalising factor of : √18 - √50
Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`
Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`
If x = 2√3 + 2√2 , find : `( x + 1/x)^2`
If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x2 - y2.
Evaluate : `( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`
Rationalise the denominator `5/(3sqrt(5))`
Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`
