3 सिद्ध कीजिए कि- 12 1.1623 al CBSE 2012...

3 सिद्ध कीजिए कि- 12 1.1623 al CBSE 2012 MP. 2009,10,15 2 .3 C C =(a-b)(b-c)(c-a)(ab+bc+ca). cthl

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|{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)

prove that , |{:(a,a^2,a^3+bc),(b,b^2,b^3+ca),(c,c^2,c^3+ab):}|=(a-b)(b-c)(c-a)(abc+bc+ca+ab)

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

det[[1,bc,bc(b+c)1,ca,ca(c+a)1,ab,ab(a+b)]]=0

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

If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca)..

Show that |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(ab+bc+ca)