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.
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 p : q = r : s; then show that: mp + nq : q = mr + ns : s.
If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`
If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Find two numbers whose mean proportional is 18 and the third proportional is 486.
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
Determine if the following numbers are in proportion:
150, 200, 250, 300
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?
Which of the following ratios are in proportion?
