Advertisements
Advertisements
Question
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)`.
Advertisements
Solution
Let `x/a = y/b = z/c = k` ...[By k method]
x = ak, y = bk and z = ck.
L.H.S.
= `(a^3k^3)/(a^2) + (b^3k^3)/(b^2) + (c^3k^3)/(c^2)`
⇒ k3 [a + b + c]
R.H.S.
= `[ak + bk + ck]^3/[a + b + c]^2`
⇒ `(k^3[a + b + c]^3)/[a + b + c]^2`
= k3 (a + b + c)
L.H.S. = R.H.S.
Hence proved.
RELATED QUESTIONS
What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
What number must be added to each of the number 16, 26 and 40 so that the resulting numbers may be in continued proportion?
What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Find the fourth proportional to 1.5, 2.5, 4.5
Find the mean proportion of: `(1)/(12) and (1)/(75)`
If 48 boxes contain 6000 pens, how many such boxes will be needed for 1875 pens?
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
