Advertisements
Advertisements
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)`.
Advertisements
उत्तर
Since a, b, c are in continued proportion,
`a/b = b/c`
`=>` b2 = ac
Now, (a2 + b2)(b2 + c2) = (a2 + ac)(ac + c2)
= a(a + c) c(a + c)
= ac(a + c)2
= b2(a + c)2
`=>` (a2 + b2)(b2 + c2) = [b(a + c)][b(a + c)]
`=> (a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`
APPEARS IN
संबंधित प्रश्न
Find the value of the unknown in the following proportion :
`1/2 : "m" :: 14/9 : 4/3`
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
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?
Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)
Choose the correct answer from the given options :
The mean proportional between `(1)/(2)` and 128 is
Are the following statements true?
40 persons : 200 persons = ₹ 15 : ₹ 75
