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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
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
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
If a, b, c are in continued proportion and a(b - c) = 2b, prove that `a - c = (2(a + b))/a`
Find the mean proportional between :
17.5 and 0.007
The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find K.
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
If a, b, c and dare in continued proportion, then prove that
`sqrt (("a + b + c")("b + c + d")) = sqrt "ab" + sqrt "bc" + sqrt "cd"`
Determine if the following numbers are in proportion:
4, 6, 8, 12
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
Determine if the following are in proportion.
32, 48, 70, 210
