Advertisements
Advertisements
प्रश्न
If a, b, c are in continued proportion, prove that a : c = (a2 + b2) : (b2 + c2).
Advertisements
उत्तर
a, b and c are the continued proportion
a: b = b: c
⇒ `a/b = b/c`
⇒ b2 = ac
Now `a/c = (a^2 + b^2)/(b^2 + c^2)`
= a(b2 + c2) = c(a2 + b2)
L.H.S.
⇒ a(b2 + c2)
⇒ a(ac + c2)
⇒ ac(a + c)
R.H.S.
⇒ c(a2 + b2)
⇒ c(a2 + ac)
⇒ ac(a + c)
L.H.S. = R.H.S.
Hence proved.
संबंधित प्रश्न
What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Find the fourth proportional to 1.5, 2.5, 4.5
Find the third proportional to 0.24, 0.6
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Verify the following:
60 : 105 : : 84 : 147
Determine if the following ratio form a proportion:
39 litres : 65 litres and 6 bottles : 10 bottles
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If a, b, c, d are in continued proportion, prove that: (a2 – b2) (c2 – d2) = (b2 – c2)2
Find the missing number in the box in the proportion:
`square/18 = 2/9`
If b : a = c : d, then a, b, c, d are in proportion.
