Advertisements
Advertisements
प्रश्न
If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`
Advertisements
उत्तर
a, b, c, d are in continued proportion
∴ `a/b = b/c = c/d` = k(say)
∴ c = dk, b = ck = dk2, a = bk = dk3
L.H.S.
= `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3)`
= `((dk^3)^3 + (dk^2)^3 + (dk)^3)/((dk^2)^3 + (dk)^3 + d^3)`
= `(d^3k^9 + d^3k^6 + d^3k^3)/(d^3k^6 + d^3k^3 + d^3)`
= `(d^3k^3(k^6 + k^3 + 1))/(d^3(k^6 + k^3 + 1)`
= k3
R.H.S.
= `a/d`
= `(dk^3)/d`
= k3
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?
If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.
If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`
Verify the following:
91 : 104 : : 119 : 136
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
Choose the correct statement:
The sides of a triangle are in the ratio 1 : 3 : 5 and its perimeter is 90 cm. The length of its largest side is
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?
