Advertisements
Advertisements
प्रश्न
If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`
Advertisements
उत्तर
Let `x/a = y/b = z/c = k`
x = ak, y = bk, z = ck
L.H.S.
= `x^3/a^3 - y^3/b^3 + z^3/c^3`
⇒ `(a^3k^3)/a^3 - (b^3k^3)/b^3 - (c^3k^3)/c^3`
⇒ k3 - k3 + k3= k3
R.H.S.
= `(xyz)/(abc)`
⇒ `(ak·bk·ck)/(abc)`
⇒ `(k^3abc)/(abc)`
= k3
L.H.S. = R.H.S.
Hence proved.
संबंधित प्रश्न
Using properties of proportion, solve for x:
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
Find the value of the unknown in the following proportion :
c
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
Find the value of x in the following proportions : 10 : 35 = x : 42
Choose the correct answer from the given options :
If x, 12, 8 and 32 are in proportion, then the value of x is
Find the missing number in the box in the proportions:
`3/8 = square/20`
The length and breadth of a school ground are 150 m and 90 m respectively, while the length and breadth of a mela ground are 210 m and 126 m, respectively. Are these measurements in proportion?
Write True (T) or False (F) against the following statement:
0.9 : 0.36 : : 10 : 4
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
25 cm : 1 m and ₹ 40 : ₹ 160
