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प्रश्न
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
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उत्तर
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)`
= `(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) xx (3sqrt(2) + 2sqrt(3))/(3sqrt(2) + 2sqrt(3)`
= `((sqrt(2) + sqrt(3))(3sqrt(2) + 2sqrt(3)))/((3sqrt(2))^2 - (2sqrt(3))^2`
= `(sqrt(2)(3sqrt(2) + 2sqrt(3)) + sqrt(3)(3sqrt(2) + 2sqrt(3)))/((9 xx 2) - (4 xx 3))`
= `((3 xx 2 + 2sqrt(6)) + (3sqrt(6) + 2 xx 3))/(18 - 12)`
= `(6 + 2sqrt(6) + 3sqrt(6) + 6)/(6)`
= `(12 + 5sqrt(6))/(6)`
= `2 - (-5/6)sqrt(6)`
= `"a" - "b"sqrt(6)`
Hence, a = 2 and b = `-(5)/(6)`.
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संबंधित प्रश्न
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`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(7 + 4sqrt(3))`, find the value of
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If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
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Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
