Advertisements
Advertisements
प्रश्न
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
Advertisements
उत्तर
`x^3 + (1)/x^3`
`(x^3 + (1)/x^3) = (x + (1)/x)^3 - 3(x + (1)/x)` ...(1)
We will first find out `x + (1)/x`
`x + (1)/x = (7 + 4sqrt(3)) + (1)/((7 + 4sqrt(3))`
= `((7 + 4sqrt(3))^2 + 1)/((7 + 4sqrt(3))`
= `(49 + 48 + 56sqrt(3) + 1)/((7 + 4sqrt(3))`
= `(98 + 56sqrt(3))/((7 + 4sqrt(3))`
= `(14(7 + 4sqrt(3)))/((7 + 4sqrt(3))`
= 14
Substituting in (1)
`(x^3 + (1)/x^3) = (x + (1)/x)^3 - 3(x + (1)/x)`
= (14)3 – 3 × 14
= 2744 – 42
= 2702
∴ `(x^3 + (1)/x^3) = 2702`
संबंधित प्रश्न
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Draw a line segment of length `sqrt5` cm.
