Show that ` {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab `

Prove that {:|(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Show that |(1+a,1, 1),(1, 1+b, 1), (1, 1,1+a)|=(1)/(a)+(1)/(b)+(1)/(c )+1 .

Evaluate Delta = {:|(1,a,bc),( 1,b,ca),(1,c,ab)|:}

Evaluate Delta -|(1,a,bc),(1,b,ca),(1,c,ab)|

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1],[1,1, 1+c]|=0 , then (1)/(a)+(1)/(b)+(1)/(c)=

Prove that |(1,1,1),(a,b,c),(a^3,b^3,c^3)| = (a - b)(b-c)(c-a)(a+b+c) .

Prove that |(1,1,1),(bc,ca,ab),(b+c, c+a, a+b)| = (a-b)(b-c)(c-a)

Prove that |{:(,1,a,a^(2)),(,1,b,b^(2)),(,1,c,c^(2)):}|=(a-b)(b-c)(c-a)

In a triangle A BC, (1)/(bc) + (1)/(ca) + (1)/(ab) = (k)/(2) , then k=