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प्रश्न
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
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उत्तर
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
= `((sqrt(5) - 2)^2 - (sqrt(5) + 2)^2)/((sqrt(5) + 2)(sqrt(5) - 2)`
= `(5 + 4 - 4sqrt(5) - 5 - 4 - 4sqrt(5))/((sqrt(5))^2 - (2)^2`
= `(-8sqrt(5))/(5 - 4)`
= `-8sqrt(5)`
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संबंधित प्रश्न
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
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Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
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(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
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`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
