Advertisements
Advertisements
Question
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"`
Advertisements
Solution
`x/a = y/b = z/c`
∴ x = ak, y = bk, z = c
L.H.S. = `[(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3`
= `[(a^2.a^2k^2 + b^2.b^2l^2 + c^2.c^2k^2)/(a^3.a.k + b^3.bk + c^3.ck)]^3`
= `[(a^4k^2 + b^4k^2 + c^4k^2)/(a^4k + b^4k + c^4k)]^3`
= `[(k^2(a^4 + b^4 + c^4))/(k(a^4 + b^4 + c^4))]^3` = k3
R.H.S. = `"xyz"/"abc"`
= `"ak.bk.ck"/"abc"` = k3
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).
If `a/c = c/d = e/f` prove that: `(a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6`
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?
Determine if the following are in proportion.
32, 48, 70, 210
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
39 litres : 65 litres and 6 bottles : 10 bottles
