Advertisements
Advertisements
Question
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
Advertisements
Solution
Let `a/b = c/d = r/f = k`
∴ a = bk, c = dk, e = fk
L.H.S.
= `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2)`
= `((b^2k^2·b^2 + d^2k^2·d^2 + f^2k^2·f^2)/(bk.b^3 + dk·d^3 + fk·f^3))^(3/2)`
= `[(k^2 (b^4 + d^4 + f^4))/(k (b^4 + d^4 + f^4))]^(3/2)`
= `k^(3/2)`
R.H.S. = `sqrt((ace)/(bdf)) = sqrt((bk·dk·fk)/(bdf)) = k^(3/2)`
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
RELATED QUESTIONS
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2 + y2 and y2 + z2.
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Find the third proportional to `5(1)/(4) and 7.`
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 `x/a = y/b = z/c`, prove that `[(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3 = "xyz"/"abc"`
Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?
The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.
| x | A | 24 | 15 |
| y | 12 | B | 20 |
The values of A and B are:
