Askiitians_Expert Yagyadutt
Last Activity: 14 Years ago
Hiii chanchal....it is very easy.....just a small trick you have to apply ..
Let a = p -d
b = p
c = p + d
now a b c are in AP with common difference ....d ..
1) 2 (a-b) = a-c = 2 (b-c)
a-b = - d
a - c = -2d
b -c = - d
so it proved from their value ...that 2(a-b) = a-c = 2(b-c)
2)(a-c)^2 = 4(b^2-ac)
(a-c) = -2d => (a-c)^2 = 4d^2
ac = ( p-d)(p+d) = p^2 -d^2
b^2 = p^2
b^2 - ac = d^2
4(b^2-ac) = 4d^2
hence ....4(b^2-4ac) = (a-c)^2 ....proved ..
Let me know if solution is insufficient for understanding....i will describe it more ..
Regards
Yagya
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