Advertisements
Advertisements
प्रश्न
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`
उत्तर
`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
संबंधित प्रश्न
If p : q = r : s; then show that: mp + nq : q = mr + ns : s.
Find the mean proportional between :
17.5 and 0.007
Find the mean proportion of the following :
ab3 and a3b
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
If `a/c = c/d = c/f` prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
Bachhu Manjhi earns Rs. 24000 in 8 months. At this rate, how much does he earn in one year?
Determine if the following are in proportion.
15, 45, 40, 120
