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Question
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
Solution
Let the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)` be x.
`\implies 6 + 3sqrt(3), x` and `8 - 4sqrt(3)` are in continued proportion.
`\implies 6 + 3sqrt(3) : x = x : 8 - 4sqrt(3)`
`\implies x xx x = (6 + 3sqrt(3)) (8 - 4sqrt(3))`
`\implies x^2 = 48 + 24sqrt(3) - 24sqrt(3) - 36`
`\implies x^2 = 12`
`\implies x = 2sqrt(3)`
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