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प्रश्न
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
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उत्तर
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
= `((4 + sqrt(5))^2 + (4 - sqrt(5))^2)/((4 - sqrt(5))(4 + sqrt(5))`
= `(16 + 5 + 8sqrt(5) + 16 + 5 - 8sqrt(5))/(16 - 5)`
= `(42)/(11)`
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संबंधित प्रश्न
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
