Advertisements
Advertisements
Question
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
Advertisements
Solution
`x^2 + (1)/x^2`
`(x^2 + (1)/x^2) = (x + (1)/x)^2 -2` ----(1)
we will first find the value of `x + (1)/x`
`x + (1)/x = (4 - sqrt(15)) + (1)/((4 - sqrt(15))`
= `((4 - sqrt(15))^2 + 1)/((4 - sqrt(15))`
= `(16 + 15 - 8sqrt(15) + 1)/((4 - sqrt(15))`
= `(8(4 - sqrt(15)))/((4 - sqrt(15))`
= 8
substituting the valuesin (1)
`(x^2 + (1)/x^2) = (x + (1)/x)^2 -2`
= 82 - 2
= 64 - 2
= 62
`(x^2 + (1)/x^2)` = 62
APPEARS IN
RELATED QUESTIONS
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
Draw a line segment of length `sqrt5` cm.
Using the following figure, show that BD = `sqrtx`.
