Advertisements
Advertisements
प्रश्न
If a, b, c, d are in continued proportion, prove that: (a2 – b2) (c2 – d2) = (b2 – c2)2
Advertisements
उत्तर
a, b, c, d are in continued proportion
∴ `a/b = b/c = c/d` = k(say)
∴ c = dk, b = ck = dk. k = dk2,
a = bk = dk2. k = dk3
L.H.S. = (a2 – b2) (c2 – d2)
= [(dk3)2 – (dk2)2] [(dk)2 – d2]
= (d2k6 – d2k4) (d2k2 – d2)
= d2k4 (k2 – 1) d2(k2 – 1)
= d4k4 (k2 – 1)2
R.H.S. = (b2 – c2)2
= [(dk2)2 – (dk)2]2
= [d2k2 – d2k2]2
= [d2k2 (k2 – 1)]2
= d4k4(k2 – 1)2
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
Find the third proportional to:
x - y, x2 - y2
Find the third proportional to Rs. 3, Rs. 12
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
Determine if the following ratio form a proportion:
200 mL : 2.5 L and Rs 4 : Rs 50
Show that the following numbers are in continued proportion:
36, 90, 225
If 48 boxes contain 6000 pens, how many such boxes will be needed for 1875 pens?
The ratio 92 : 115 in its simplest for is
5 : `square` : : 10 : 8 : : 15 : `square`
If 7 : 5 is in proportion to x : 25, then ‘x’ is
