Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+...

Prove that `| ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2abc(a+b+c)^3`

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Prove that ,,(b+c)^(2),a^(2),a^(2)b^(2),(c+a)^(2),b^(2)c^(2),c^(2),(a+b)^(2)]|=2abc(a+b+c)^(3)

Prove that: ,,(b+c)^(2),a^(2),a^(2)b^(2),(c+a)^(2),b^(2)c^(2),c^(2),(a+b)^(2)]|=2abc(a+b+c)^(3)

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

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

Prove that |[(a+b)^(2),ca,bc],[ca,(b+c)^(2),ab],[bc,ab,(c+a)^(2)]|=2abc(a+b+c)^(3)

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

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

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

Prove that |[a,b,c] , [a^2,b^2,c^2] , [a^3,b^3,c^3]|= abc(a-b)(b-c)(c-a)

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

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))

For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...
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|(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)
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Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3
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|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|
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Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot
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Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...
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Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0
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Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, ...
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Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/...
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Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2)...
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Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...
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|[(b+c)^2,ab,ca],[ab,(a+c)^2,bc],[ac,bc,(a+b)^2]|=2abc(a+b+c)^3
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Show that Delta=|(y+z)^2x y z xx y(x+z)^2y z x z y z(x+y)^2|=2x y z(x+...
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If a, b, c are positive and unequal, show that value of the determinan...
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Using properties of determinants, prove that |a a+b a+b+c2a3a+2b4a...
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Using properties of determinants. Prove that |1 1+p1+p+q2 3+2p4+3p+2q3...
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Q. |(x+y,x,x),(15x+4y,4x,2x),(10x +8y,8x,3x)|=x^3
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Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...
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Prove that |{:(a^(2), a^(2)-(b-c)^(2), bc), (b^(2), b^(2)-(c-a)^(2), ...
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If p, q, r are not in G.P. and |[1,q/p,alpha+q/p],[1,r/p,alpha+r/q],[p...
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