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
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?
In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
39 litres : 65 litres and 6 bottles : 10 bottles
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.
