Advertisements
Advertisements
प्रश्न
Find the fourth proportion to the following :
(x2 - y2),(x3 + y3)anc(x3 - xy2 + x2y- y3)
Advertisements
उत्तर
Let z be the fourth proportion
(x2 -y3) (x3 + y3) :: (x3 - xy2 + x2y - y3) : z
⇒ (x2 - y2 ) z = (x3 + y3)(x3- xy2 + x2y -y3)
⇒ z = `(("x"^3 + "y"^3)("x"^3 - "xy"^2 + "x"^2"y" - "y"^3))/("x"^2 - "y"^2)`
⇒ z = `(("x" + "y")("x"^2 - "xy"^2 + "x"^2"y" - "y"^3))/(("x + y")("x - y"))`
⇒ z = (x2 - xy + y2)(x + y)2
Therefore . the fourth proportion is (x2 + y2 - xy)(x + y)2
APPEARS IN
संबंधित प्रश्न
The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find k.
If 15 tins of the same size contain 234 kg of oil, how much oil will there be in 10 such tins?
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
If a, b, c are in continued proportion, prove that: (a + b + c) (a – b + c) = a2 + b2 + c2
If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)2
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)`.
12 : `square` = `square` : 4 = 8 : 16
If 7 : 5 is in proportion to x : 25, then ‘x’ is
