Advertisements
Advertisements
Question
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
Advertisements
Solution
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.
RELATED QUESTIONS
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.
If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.
Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?
If `1/12` , x and `1/75` are in continued proportion , find x.
If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`
Verify the following:
39 : 65 : : 141 : 235
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
If a, b, c are in proportion, then
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
Find the missing number in the box in the proportions:
`3/8 = square/20`
