Advertisements
Advertisements
प्रश्न
If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)
Advertisements
उत्तर
As a, b, c, are in continued proportion
Let `a/b = b/c` = k
a : c = (a2 + b2) : (b2 + c2)
⇒ `a/c = (a^2 + b^2)/(b^2 + c^2)`
L.H.S. = `a/c`
= `(ck^2)/c`
= k2
R.H.S. = `((ck^2)^2 + (ck)^2)/((ck)^2 + c^2)`
= `(c^2k^4 + c^2k^2)/(c^2k^2 + c^2)`
= `(c^2k^2(k^2 + 1))/(c^2(k^2 + 1)`
=k2
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If (a2 + b2)(x2 + y2) = (ax + by)2; prove that: `a/x = b/y`.
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
If a, b, c and dare in continued proportion, then prove that
`sqrt (("a + b + c")("b + c + d")) = sqrt "ab" + sqrt "bc" + sqrt "cd"`
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Find the mean proportion of: `(1)/(12) and (1)/(75)`
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
If a, b, c are in proportion, then
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
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
25 cm : 1 m and ₹ 40 : ₹ 160
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
