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
If (a2 + b2)(x2 + y2) = (ax + by)2; prove that: `a/x = b/y`.
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
Verify the following:
108 : 72 : : 129 : 86
Verify the following:
39 : 65 : : 141 : 235
Determine if the following ratio form a proportion:
25 cm : 1 m and Rs 40 : Rs 160
The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is
If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
