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प्रश्न
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
उत्तर
`(5 + 2sqrt(3))/(7 + 4sqrt(3)`
= `(5 + 2sqrt(3))/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3)`
= `(5(7 - 4sqrt(3)) + 2sqrt(3)(7 - 4sqrt(3)))/((7)^2 - (4sqrt(3))^2`
= `(35 - 20sqrt(3) + 14sqrt(3) - 24)/(49 - 48)`
= `(11 - 6sqrt(3))/(1)`
= `11 + (-6)sqrt(3)`
= `"a" + "b"sqrt(3)`
Hence, a = 11 and b = -6
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संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
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Simplify :
` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`
Simplify by rationalising the denominator in the following.
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`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
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`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
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In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
If x = `(4 - sqrt(15))`, find the values of
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