Advertisements
Advertisements
प्रश्न
If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.
Advertisements
उत्तर
Let `a/b = c/d = e/f = k` then
a = bk, c = dk and e = fk
L.H.S.
= (ab + cd + ef)2
= (bk·b + dk·d + fk·f)2
= k2 (b2 + d2 + f2)2
R.H.S.
= (a2 + c2 + e2)(b2 + d2 + f2)
= (b2k2 + d2k2 + f2k2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)2.
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x2+ y2 and y2+ z2
Find the fourth proportional to:
2xy, x2, y2
If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`
Determine if the following numbers are in proportion:
33, 121, 9, 96
Determine if the following ratio form a proportion:
25 cm : 1 m and Rs 40 : Rs 160
An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8 m. Find the height of the pole.
Find the value of x if 5 : 3 : : x : 6.
Find the missing number in the box in the proportion:
`8/square = 3.2/4`
Are the following statements true?
45 km : 60 km = 12 hours : 15 hours
