Advertisements
Advertisements
प्रश्न
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Advertisements
उत्तर
Let x be the fourth proportion
`("p"^2"q" - "qr"^2) : ("pqr" - "pr"^2) :: ("pq"^2 - "pr"^2) : x`
⇒ `("p"^2"q" - "qr"^2) xx "x" = ("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2)`
⇒ x = `(("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2))/(("p"^2"q" - "qr"^2))`
⇒ x = `("pr"("q" - "r") xx "p"("q"^2 - "r"^2))/("q"("p"^2 - "r"^2))`
⇒ x = `("pr"("q - r") xx "p"("q - r")("q + r"))/("q"("p"^2 - "r"^2))`
⇒ x = `("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))`
The fourth proportion is `("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))`
APPEARS IN
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2 + 11n^2)`
Find the mean proportional of the following:
17.5, 0.007
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall?
The ratio 92 : 115 in its simplest for is
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
Are the following statements true?
45 km : 60 km = 12 hours : 15 hours
