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
Given four quantities a, b, c and d are in proportion. Show that: (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
Find the third proportion to the following :
`9/25` and `18/25`
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?
A given quantity of rice is sufficient for 60 persons for 3 days. How many days would the rice last for 18 persons?
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.
Are the following statements true?
99 kg : 45 kg = ₹ 44 : ₹ 20
