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Question
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
Options
1
–1
`2sqrt(2)`
3
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Solution
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is 1.
Explanation:
Mean proportion between x and y = `sqrt(xy)`
∴ Mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)`
= `sqrt((3 + 2sqrt(2))(3 - 2sqrt(2))`
= `sqrt(3^2 - (2sqrt(2))^2)` ...[∵ (a + b)(a – b) = a2 – b2]
= `sqrt(9 - 8)`
= `sqrt(1)`
= 1
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