" 18.यदि "(b-c)^(2),(c-a)^(2),(a-b)^(2)" समांतर श्रेढ़ी में है,तो सिद्ध करो "(1)/(b-c),(1)/(c-a),(1)/(a-b)" समांतर श्रेढ़ी में होंगे। "

1,1,1a,b,ca^(2),b^(2),c^(2)]|=(a-b)(b-c)(c-a)

([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

if a+b+c = 0, then ((2a^2)/(3bc)+ (2b^2)/(3ca)+(2c^2)/(3ab)) is equal to: यदि a+b+c = 0 है, तो ((2a^2)/(3bc)+ (2b^2)/(3ca)+(2c^2)/(3ab)) बराबर है :

|[1, b+c, b^(2)+c^(2)], [1, c+a, c^(2)+a^(2)], [1, a+b, a^(2)+b^(2)]| = (a-b)(b-c)(c-a)

|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)

(1)/(c),(1)/(c),-(a+b)/(c^(2))-(b+c)/(c^(2)),(1)/(a),(1)/(a)(-b(b+c))/(a^(2)c),(a+2b+c)/(ac),(-b(a+b))/(ac^(2))]| is

If a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1 , then show that 1/(1+a) + 1/(1 + b) + 1/(1+c) = 1 .