Advertisements
Advertisements
Question
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
Advertisements
Solution
x = `((2 + sqrt(5)))/((2 - sqrt(5))`
= `((2 + sqrt(5)))/((2 - sqrt(5))) xx ((2 + sqrt(5)))/((2 + sqrt(5))`
= `(2 + sqrt(5))^2/(4 - 5)`
= `-(4 + 5 + 4sqrt(5))`
= `-9 -4sqrt(5)`
y = `((2 - sqrt(5)))/((2 + sqrt(5))`
= `((2 - sqrt(5)))/((2 + sqrt(5))) xx ((2 - sqrt(5)))/((2 - sqrt(5))`
= `(2 - sqrt(5))^2/(4 - 5)`
= `-(4 + 5 -4sqrt(5))`
= `-9 + 4sqrt(5)`
∴ x2 - y2 = (x + y) (x - y)
= `(-9 - 4sqrt(5) - 9 + 4sqrt(5))(-9 -4sqrt(5) + 9 - 4sqrt(5))`
= `(-18)(-8sqrt(5))`
= `144sqrt(5)`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
Show that Negative of an irrational number is irrational.
