Advertisements
Advertisements
प्रश्न
If `x/a = y/b = z/c`, prove that `(3x^3 - 5y^3 + 4z^3)/(3a^3 - 5b^3 + 4c^3) = ((3x - 5y + 4z)/(3a - 5b + 4c))^3`.
Advertisements
उत्तर
`x/a = y/b = z/c` = k(say)
x = ak, y = bk, z = ck
L.H.S. = `(3x^3 5y^3 + 4z^3)/(3a^3 5b^3 + 4c^3)`
= `(3a^3k^3 - 5b^3k^3 + 4c^3k^3)/(3a^3 - 5b^3 + 4ac^3)`
= `(k^3(3a^3 - 5b^3 + 4c^3))/(3a^3 - 5b^3 + 4c^3`
= k3
R.H.S. = `((3x - 5y + 4z)/(3a - 5b + 4c))^3`
= `((3ak - 5bk + 4ck)/(3a - 5b + ac))^3`
= `((k(3a - 5b + 4c))/(3a - 5b + 4c))^3`
= (k)3
= k3
∴ L.H.S. = R.H.S.
संबंधित प्रश्न
Find the ratio of 50 paise to Rs 5.
If A : B = 2 : 5 and A : C = 3 : 4, find: A : B : C.
If (3x - 9) : (5x + 4) is the triplicate ratio of 3 : 4, find the value of x.
Two numbers are in the ratio 9 : 2. If the smaller number is 320, find the larger number.
Ratio of the distance of the school from A’s home to the distance of the school from B’s home is 2 : 1.
(i) Who lives nearer to the school?
(ii) Complete the following table:
Which ratio is greater:
`3/7` or `6/13`
The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg; find the weight of copper in the alloy.
Find the sub-triplicate ratio of `(1)/(8) : (1)/(125)`
Mr. Sahai and his wife are both school teachers and earn Rs 16800 and Rs 10500 per month respectively. Find the ratio of
(i) Mr. Sahai's income to his wife's income;
(ii) Mrs. Sahai's income to her husband's income;
(iii) Mr. Sahai's income to the total income of the two.
Choose the correct answer from the given options :
The ratio of 4 litres to 900 mL is
