Advertisements
Advertisements
Question
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^3/b^2 + z^3/c^2 = (x+ y+ z)^3/(a + b+ c)^2`
Advertisements
Solution
`x/a = y/b = z/c`
∴ x = ak, y = bk, z = ck
L.H.S. = `x^3/a^2 + y^3/b^2 + z^3/c^2`
= `(a^3k^3)/a^2 + (b^3k^3)/(b^2) + (c^3k^3)/c^2`
= ak3 + bk3 + ck3
= k3(a + b + c)
R.H.S. = `(x + y + z)^3/(a + b + c)^2`
= `(ak + bk + ck)^3/(a + b + c)^2`
= `(k^3(a + b + c)^3)/((a + b + c)`
= k3(a + b + c)
Hence L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
Determine if the following numbers are in proportion:
22, 33, 42, 63
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
If 7 : 5 is in proportion to x : 25, then ‘x’ is
Bachhu Manjhi earns Rs. 24000 in 8 months. At this rate, how much does he earn in one year?
Write True (T) or False (F) against the following statement:
21 : 6 : : 35 : 10
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
