If `=|a b c b^2cc^2b a b cc^2a c a^2a b c a^2bb^2a|=0,(a ,b ,c in R` and are all different and nonzero), then prove that `a+b+c=0.`

Prove: |b+c a a b c+a b cc a+b|=4a b c

Prove that |b+c a a b c+a b cc a+b|=4a b c

If =det[[abc,b^(2)c,c^(2)babc,c^(2)a,ca^(2)abc,c^(2)a,ca^(2)abc,a^(2)b,b^(2)a]]=0,(a,b,c in R) and a+b+c,=0a+b+c,=0

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) , where a,b,c gt 0 .

Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a b,-a b)|=(a b+b c+c a)^3

If |0a b^2a c^2a^2b0b c^2a^2cc b^2 0|=2a^pb^q c^r ,t h e np+q+r+10 is equal to 27 (b) 18 (c) 19 (d) 8

If (b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b) are in A.P. and a+b+c=0 then prove that a(b+c-a),b(c+a-b),c(a+b-c) are in A.P.