Advertisements
Advertisements
प्रश्न
If q is the mean proportional between p and r, prove that: p3 – 3q2 + r2 = `q^4(1/p^2 - 3/q^2 + 1/r^2)`
Advertisements
उत्तर
q is mean proportional between p and r
q² = pr
L.H.S. = p2 – 3q2 + r2 = p2 – 3pr + r2
R.H.S. = `q^4(1/p^2 - 3/q^2 + 1/r^2)`
= `(q^2)^2(1/p^2 - 3/q^2 + 1/r^2)`
= `(pr)^2(1/p^2 - 3/q^2 + 1/r^2)`
= `(pr)^2(1/p^2 - 3/"pr" + 1/r^2)`
= `p^2r^2((r^2 - 3pr + p^2)/(p^2r^2))`
= r2 - 3pr + p2
∴ L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the third proportion to the following :
`9/25` and `18/25`
If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
A labourer earns Rs 1980 in 12 days.
(i) How much does he earn in 7 days?
(ii) In how many days will he earn Rs 2640?
Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed
