Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a^2 + ab + b^2)/(a^2 - ab + b^2)`
= `(b^2k^2 + bk.b + b^2)/(b^2k^2 - bk.b + b^2)`
= `(b^2(k^2 + k + 1))/(b^2(k^2 - k + 1)`
= `(k^2 + k + 1)/(k^2 - k + 1)`
R.H.S. = `(c^2 + cd + d^2)/(c^2 - cd + d^2)`
= `(d^2k^2 + dkd + d^2)/(d^2k^2 - dk.d + d^2)`
= `(d^2(k^2 + k + 1))/(d^2(k^2 - k + 1)`
= `(k^2 + k + 1)/(k^2 - k + 1)`
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`
Find the value of the unknown in the following proportion :
5 : 12 :: 15 : x
Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`
If a, 12, 16 and b are in continued proportion find a and b.
What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?
Verify the following:
60 : 105 : : 84 : 147
A car travels 195 km in 3 hours.
(i) How long will it take to travel 520 km?
(ii) How far will it travel in 7 hours at the same speed?
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: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
Find two numbers whose mean proportional is 16 and the third proportional is 128.
