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प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
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उत्तर
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
`= (sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3) xx (sqrt 5 - sqrt 3)/(sqrt 5 - sqrt 3)`
`= (sqrt 5 - sqrt 3)^2/((sqrt 5)^2 - (sqrt 3)^2) ....[because (a + b)(a - b) = a^2 - b^2]`
`= ((sqrt 5)^2 - 2(sqrt 5)(sqrt 3) + (sqrt 3)^2)/(5-3) ...[because (a - b)^2 = a^2 - 2ab + b^2]`
`= (5 - 2sqrt15 + 3 )/2`
`= (8 - 2sqrt 15)/2`
`= (2 (4 - sqrt15))/2`
`= 4 -sqrt15`
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In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
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`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
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`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
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`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
