Prove the following : |(1,x,x^(2)-yz),(...

Prove the following : `|(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0`.

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Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.

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

|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc
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Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=...
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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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