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प्रश्न
Given four quantities a, b, c and d are in proportion. Show that: (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)
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उत्तर
Let `a/b = c/d = k`
`=>` a = bk and c = dk
L.H.S = `((a - c)b^2)/((b -d)cd)`
= `((bk - dk)b^2)/((b - d)d^2k)`
= `b^2/d^2`
R.H.S = `(a^2 - b^2 - ab)/(c^2 - d^2 - cd)`
= `(b^2k^2 - b^2 - bkb)/(d^2k^2 - d^2 - dkd)`
= `(b^2(k^2 - 1 - k))/(d^2(k^2 - 1 - k))`
= `b^2/d^2`
`=>` L.H.S = R.H.S
Hence proved.
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What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Write (T) for true and (F) for false in case of the following:
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(i) How long will it take to travel 520 km?
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