If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2...

If `|{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez ,` prove that, xyz=-1.

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

Factorise : |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|
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|{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|
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If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...
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Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...
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Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...
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prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...
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Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...
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|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc
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|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...
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|{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...
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|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)
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|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3
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|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
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|{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...
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|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
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|{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...
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prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...
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If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...
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If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...
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without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...
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