Advertisements
Advertisements
प्रश्न
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Advertisements
उत्तर
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3)`
`= (4 - sqrt5)/(4 + sqrt5) xx (4 - sqrt5)/(4 - sqrt5) + 2/(5 + sqrt3) xx (5 - sqrt3)/(5 - sqrt3) + (4 + sqrt5)/(4 - sqrt5) xx (4 + sqrt5)/(4 + sqrt5) + 2/(5 - sqrt3) xx (5 + sqrt3)/(5 + sqrt3)`
`= (4 - sqrt5)^2/((4)^2 - (sqrt5)^2) + (2(5 - sqrt3))/((5)^2 - (sqrt3)^2) + (4 + sqrt5)^2/((4)^2 - (sqrt5)) + (2(5 + sqrt3))/((5)^2 - (sqrt3)^2)`
`= (16 + 5 - 8sqrt5)/(16 - 5) + (10 - 2sqrt3)/(25 - 3) + (16 + 5 + 8sqrt5)/(16 - 5) + (2(5 + sqrt3))/(25 - 3)`
`= (21 - 8sqrt5)/11 + (10 - 2sqrt3)/22 + (21 + 8sqrt5)/11 + (cancel(2)^1 (5 + sqrt3))/cancel(22)_11`
`= (21 - 8sqrt5)/11 + (cancel(2)^1(5 - sqrt3))/cancel(22)_11 + (21 + 8sqrt5)/11 + (5 + sqrt3)/11`
`= (21 - cancel(8sqrt5) + 5 - cancel(sqrt3) + 21 + cancel(8sqrt5) + 5 + cancel(sqrt3))/11`
`= (21 + 5 + 21 + 5)/11`
`= 52/11`
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
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)`
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`
