Advertisements
Advertisements
प्रश्न
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
Advertisements
उत्तर
Let the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)` be x.
`\implies 6 + 3sqrt(3), x` and `8 - 4sqrt(3)` are in continued proportion.
`\implies 6 + 3sqrt(3) : x = x : 8 - 4sqrt(3)`
`\implies x xx x = (6 + 3sqrt(3)) (8 - 4sqrt(3))`
`\implies x^2 = 48 + 24sqrt(3) - 24sqrt(3) - 36`
`\implies x^2 = 12`
`\implies x = 2sqrt(3)`
APPEARS IN
संबंधित प्रश्न
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
Find the value of the unknown in the following proportion :
5 : 12 :: 15 : x
Find the mean proportion of the following :
`28/3` and `175/27`
If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.
Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`
Write (T) for true and (F) for false in case of the following:
30 bags : 18 bags : : Rs 450 : Rs 270
If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.
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)`.
