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प्रश्न
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.
पर्याय
`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 mean proportional between a – b and a3 – a2b
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Find the third proportional to a2 – b2 and a + b.
Find the fourth proportion to the following :
(x2 - y2),(x3 + y3)anc(x3 - xy2 + x2y- y3)
Find the third proportion to the following :
`9/25` and `18/25`
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
Verify the following:
39 : 65 : : 141 : 235
If `x/a = y/b = z/c`, prove that `"ax - by"/((a + b)(x- y)) + "by - cz"/((b + c)(y - z)) + "cz - ax"/((c + a)(z - x)` = 3
Find the missing number in the box in the proportion:
`square/18 = 2/9`
