Advertisements
Advertisements
प्रश्न
If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`
Advertisements
उत्तर
`sqrt(5) + 2` ⇒ x2 = `(sqrt(5) + 2)^2`
= `(sqrt(5))^2 + 2 xx 2 xx sqrt(5) + 2^2`
= `5 + 4sqrt(5) + 4`
= `9 + 4sqrt(5)`
`1/x = 1/(sqrt(5) + 2)`
= `(sqrt(5) - 2)/((sqrt(5) + 2)(sqrt(5) - 2))`
= `(sqrt(5) - 2)/((sqrt(5))^2 - 2^2)`
= `(sqrt(5) - 2)/(5 - 4)`
= `sqrt(5) - 2`
`1/x^2 = (sqrt(5) - 2)^2`
= `(sqrt(5))^2 - 2 xx sqrt(5) xx 2 + 2^2`
= `5 - 4sqrt(5) + 4`
= `9 - 4sqrt(5)`
∴ `x^2 + 1/x^2 = 9 + 4sqrt(5) + 9 - 4sqrt(5)` = 18
The value of `x^2 + 1/x^2` = 18
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`3 /sqrt5`
Rationalize the denominator.
`1/sqrt14`
Rationalize the denominator.
`6/(9sqrt 3)`
Write the simplest form of rationalising factor for the given surd.
`sqrt 32`
Write the simplest form of rationalising factor for the given surd.
`4 sqrt 11`
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y2
If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find mn
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.
Rationalise the denominator `1/sqrt(50)`
