If `a,b,c>0` and `x,y,z in R` then `|[(a^x+a^(-x))^2, (a^x-a^(-x))^2, 1] , [(b^y+b^(-y))^2, (b^y-b^(-y))^2, 1], [(c^z+c^(-z))^2, (c^z-c^(-z))^2, 1]|`=

If a, b,c> 0 and x,y,z in R then the determinant: |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to

Prove that the value of each the following determinants is zero: (a^(x)+a^(-x))^(2),(a^(x)-a^(-x))^(2),1(b^(y)+b^(-y))^(2),(b^(y)-+b^(-y))^(2),1(c^(z)+c^(-z))^(2),(c^(z)-c^(-z))^(2),1]|

If a, b, c > 0 and x, y, z E R, then the determinant (a +a*)2 (a -ax)2 1 (b + b-y)2 (b b-y)2 1 (c2 + c2)2 (c+c2)2 1 x12 al roots of = 0, is is dependent on a. a, b, c only c. a, b, c, x, y, z b. x, y, z only d. None of these (-9: Let x < 1? then value of x2 +2 2x +1 1

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)

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

If x+a=y+b+1=z+c then the value of [[x, (a+y), (a+x)], [y, (b+y), (b+y)], [z, (c+y), (c+z)]] is

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(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),,(c-z)^(2)):}| |{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}| =2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)