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
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Simplify :
` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Draw a line segment of length `sqrt3` cm.
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
