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
If `a/b = c/d` prove that each of the given ratios is equal to
`(5a + 4c)/(5b + 4d)`
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
What number must be added to each of the number 16, 26 and 40 so that the resulting numbers may be in continued proportion?
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
Find the fourth proportional to:
2xy, x2, y2
Find the fourth proportional to:
x3 - y2, x4 + x2y2 + y4, x - y.
If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.
A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not
Determine if the following are in proportion.
4, 6, 8, 12
Which of the following statements correctly defines a proportion involving four non-zero quantities a, b, c, and d?
