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 p, q and r in continued proportion, then prove the following :
`"p"^2 - "q"^2 + "r"^2 = "q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Find the third proportional to:
x - y, x2 - y2
If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.
Determine if the following numbers are in proportion:
22, 33, 42, 63
Determine if the following ratio form a proportion:
200 mL : 2.5 L and Rs 4 : Rs 50
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
