Advertisements
Advertisements
प्रश्न
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]`.
Advertisements
उत्तर
Since, q is the mean proportional of p and r.
Hence, q2 = pr.
R.H.S. = `q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`
= `q^4[(1)/p^2 - (1)/(pr) + (1)/r^2]`
= `q^4[(r^2 - pr + p^2)/(p^2r^2)]`
= `q^4[(p^2 - pr + r^2)/(pr)^2]`
= `q^4[(p^2 - pr + r^2)/q^4]`
= p2 - pr + r2
= p2 - q2 + r2 = L.H.S.
Hence proved.
संबंधित प्रश्न
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
Find the mean proportion of: (a – b) and (a³ – a²b), a> b
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
Fill the boxes using any set of suitable numbers 6 : `square` : : `square` : 15
Determine if the following are in proportion.
15, 45, 40, 120
The first, third, and fourth terms of a proportion are 9, 24, and 32. Find the second term.
