Advertisements
Advertisements
प्रश्न
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Advertisements
उत्तर
x3 + y3
(x3 + y3) = (x + y)3 - 3xy (x + y) ----(1)
Now, x + y = `(1)/((3 - 2sqrt(2))) + (1)/((3 + 2sqrt(2))`
= `((3 + 2sqrt(2)) + (3 - 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`
= `(6)/(9 - 8)`
= 6
and xy = `(1)/((3 - 2sqrt(2))) xx (1)/((3 + 2sqrt(2))`
= `(1)/(9 - 8)`
= 1
substituting the valuesin (1), we get
(x3 + y3)
= (x + y)3 - 3xy (x + y)
= 216 - 3 x 6
= 198
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/sqrt5`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Show that Negative of an irrational number is irrational.
Draw a line segment of length `sqrt3` cm.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
