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
If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`
If (a2 + b2)(x2 + y2) = (ax + by)2; prove that: `a/x = b/y`.
Check whether the following numbers are in continued proportion.
9, 12, 16
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.
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?
If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`
Are 30, 40, 45, and 60 in proportion?
`square` : 24 : : 3 : 8
The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?
If 7 : 5 is in proportion to x : 25, then ‘x’ is
