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प्रश्न
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.
विकल्प
`sqrt(5)`
5
1
0
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उत्तर
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
संबंधित प्रश्न
Find the fourth proportional to 3a, 6a2 and 2ab2
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0.09 and 0.25
Find two numbers whose mean proportional is 18 and the third proportional is 486.
Find the third proportional to 5, 10
Determine if the following numbers are in proportion:
150, 200, 250, 300
Show that the following numbers are in continued proportion:
36, 90, 225
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
If a, b, c, d are in continued proportion, prove that: `((a - b)/c + (a - c)/b)^2 - ((d - b)/c + (d - c)/b)^2 = (a - d)^2 (1/c^2 - 1/b^2)`.
Determine if the following are in proportion.
4, 6, 8, 12
