Advertisements
Advertisements
प्रश्न
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
Advertisements
उत्तर
Given, a, b and c are in continued proportion.
Therefore,
`a/b = b/c`
ac = b2
Here,
`(a^2 + ab + b^2)/(b^2 + bc + c^2) = (a^2 + ab + ac)/(ac + bc + c^2)`
= `(a(a + b + c))/(c(a + b + c))`
= `a/c`
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the third proportional to:
x - y, x2 - y2
Find the third proportional to 5, 10
Verify the following:
39 : 65 : : 141 : 235
Show that the following numbers are in continued proportion:
16, 84, 441
Find the value of x if 5 : 3 : : x : 6.
A labourer earns Rs 1980 in 12 days.
(i) How much does he earn in 7 days?
(ii) In how many days will he earn Rs 2640?
The ratio of boys and girls in a school is 12 : 5. If the number of girls is 840, the total strength of the school is
If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.
The quarterly school fee in Kendriya Vidyalaya for Class VI is Rs. 540. What will be the fee for seven months?
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
