Advertisements
Advertisements
प्रश्न
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
Advertisements
उत्तर
x = `7 + 4sqrt(3)`
∴ `(1)/x = (1)/(7 + 4sqrt(3))`
= `(1)/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3))`
= `(7 - 4sqrt(3))/(7^2 - (4sqrt(3))^2`
= `(7 - 4sqrt(3))/(49 - 48)`
= `(7 - 4sqrt(3))/(1)`
= `7 - 4sqrt(3)`
∴ `x + (1)/x `
= `(7 + 4sqrt(3)) + (7 - 4sqrt(3))`
= `7 + 4sqrt(3) + 7 - 4sqrt(3)`
= 14
Hence, `(x + (1)/x)^2`
= (14)2
= 196
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
