Advertisements
Advertisements
प्रश्न
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
उत्तर
x = `4 - sqrt(15)`
∴ `(1)/x = (1)/(4 - sqrt(15))`
= `(1)/(4 - sqrt(15)) xx (4 + sqrt(15))/(4 + sqrt(15))`
= `(4 + sqrt(15))/(4^2 - (sqrt(15))^2`
= `(4 + sqrt(15))/(16 - 15)`
= `(4 + sqrt(15))/(1)`
= `4 + sqrt(15)`
∴ `x + (1)/x = (4 - sqrt(15)) + (4 + sqrt(15))`
= `4 - sqrt(15) + 4 + sqrt(15)`
= 8
Hence, `(x + (1)/x)^2`
= (8)2
= 64
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalize the denominator.
`12/(4sqrt3 - sqrt 2)`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
