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Question
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.
Options
`sqrt(5)`
5
1
0
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Solution
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is 1.
Explanation:
Mean proportional of `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)`
= `sqrt((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))`
= `sqrt((sqrt(3))^2 - (sqrt(2))^2` ...[∵ (a + b)(a – b) = a2 – b2]
= `sqrt(3 - 2)`
= `sqrt(1)`
= 1
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