If `a+b+c=6`;`ab+bc+ca=11`;`abc=6`, then find the value of `(1-a)(1-b)(1-c)`.
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If a+b+c=2, ab+bc+ca=-1 and abc=-2 , find the value of a^(3)+b^(3)+c^(3) .

When a=3 , b=0 , c=-2 , then find the value of : ab+2bc+3ca+4abc.

If the points (a^3/(a-1),(a^2-3)/(a-1)) , (b^3/(b-1),(b^2-3)/(b-1)) , (c^3/(c-1),(c^2-3)/(c-1)) are collinear for 3 distinct values a,b,c and a!=1, b!=1, c!=1 , then find the value of abc-(ab+bc+ca)+3(a+b+c) .

In DeltaABC, Delta = 6, abc = 60, r=1 . Then the value of (1)/(a) + (1)/(b) + (1)/(c) is nearly

If a+b+c=6 then the maximum value of sqrt(4a+1)+sqrt(4b+1)+sqrt(4c+1)=

In triangleABC , Delta=6 , abc=60 , r=1 Then the value of 1/a+a/b+a/c is nearly (a) 0.5 (b) 0.6 (c) 0.4 (d) 0.8

If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1,1 +b,1),(1,1,1 +c)| = 0 , then the value of (1)/(a) + (1)/(b) + (1)/(c) is

If a+b+c=1 , the greatest value of (ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a) , is

Find the value of the following. abc - ab-bc for a = 2, b= -3,c=-1

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If a,b, c are real and distinct numbers, then the value of ((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/((a-b).(b-c).(c-a))is