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प्रश्न
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
उत्तर
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
= `((sqrt(5) + sqrt(3))^2 + (sqrt(5) - sqrt(3))^2)/((sqrt(5) - sqrt(3))(sqrt(5) + sqrt(3))`
= `(5 + 3 + sqrt(15) + 5 + 3 - sqrt(15))/(5 - 3)`
= `(16)/(2)`
= 8
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संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
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)`
