Advertisements
Advertisements
प्रश्न
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
Advertisements
उत्तर
∵ x,y,z are in continued proportion,
`∴ x/y = y/z => y^2 = zx .....(1)`
`(x + y)/y = (y + z)/z` (By componendo)
`=> (x + y)^2/(y + z) = y/z` (By alternendo)
`=> (x + y)^2/(y + z)^2 = y^2/z^2 => (x + y)^2/(y + z)^2 = (zx)/z^2`
`=> (x + y)^2/(y + z)^2 = x/z `
Hence Proved
APPEARS IN
संबंधित प्रश्न
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find k.
If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.
Find the mean proportion of: 5 and 80
Choose the correct statement:
Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is
If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).
`square` : 24 : : 3 : 8
The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?
Write True (T) or False (F) against the following statement:
5.2 : 3.9 : : 3 : 4
