Saved Bookmarks
| 1. |
If pth,qth,rth ofan ap is a,b,c show (a-b)r+(b-c)p+(c-a)q=0 |
| Answer» A + (p - 1)D = a ......(i)A + (q - 1)D = b ....... (ii)A + (r - 1)D = c .......(iii)(ii) - (iii)b - c = (q - 1)D - (r - 1)D{tex} \\Rightarrow {/tex}\xa0b - c = D(q - r){tex} \\Rightarrow {/tex}\xa0p(b - c) = p D(q - r) ...... (iv)Similarly,q(c - a) = q D(r - p) ...... (v)r(a - b) = rD (p - q) ...... (vi)Adding (iv), (v) and (vi)p(b-c) + q(c - a) + r(a - b) = 0 | |