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Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^...

Prove that `|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=` `|(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot`

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Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x)^2),((b-y)^2),((b-z)^2)),(((c-x)^2),((c-y)^2),((c-z)^2))|

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Prove that |(b+x)(c+x)(v+x)(a+x)(a+x)(b+x)(b+y)(c+y)(c+x)(a+t)(a+y)(b+y)(b+z)(c+z)(c+z)(a+z)(a+z)(b+z)|=(b-c)(c-a)(y-z)(x-y)dot

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

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If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).

RESONANCE ENGLISH-MATRICES & DETERMINANT-HLP
  1. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  2. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

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  3. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

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  4. if (x(1)-x(2))^(2)+(y(1)-y(2))^(2)=a^(2), (x(2)-x(3))^(2)+(y(2)-y(3))^...

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  5. Let A=[{:(,cos^(-1)x, cos^(-1)y,cos^(-1)z),(,cos^(-1)y, cos^(-1)z,cos^...

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  6. If y=(u)/(v), where u and v are functions of x, show that v^(3)(d^(2...

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  7. If alpha, beta are the roots of the equation ax^(2)+bx+c=0 and S(n)=al...

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  8. Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...

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  9. Let overset(to)(a(r))=x(r )hat(i)+y(r )hat(j)+z(r )hat(k),r=1,2,3 thre...

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  10. If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3)...

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  11. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

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  12. about to only mathematics

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  13. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

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  14. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

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  15. If a,b,c are real number, and D=|{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+...

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  16. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

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  17. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

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  18. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

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  19. Let A be a (4xx4) matrix such that the sum of elements in each row is ...

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  20. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

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