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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
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalize the denominator.
`1/(sqrt 3 - sqrt 2)`
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 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`
