Advertisements
Advertisements
प्रश्न
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
Advertisements
उत्तर
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
संबंधित प्रश्न
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
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)`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
