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))|

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

Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x))^2, 1],[(a^y+a^(-y))^2,(a^y-a^(-y))^2, 1],[(a^z+a^(-z))^2,(a^z-a^(-z))^2, 1]|, where a>0 and x , y , z in R

If a, b,c> 0 and x,y,z in RR 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:

Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1(a^y+a^(-y))^2(a^y-a^(-y))^2 1(a^2+a^(-z))^2(a^z-a^(-z))^2 1|, where a , >0a n dx , y , z in Rdot

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)

If x=asecthetacosvarphi , y=bsecthetasinvarphi and z=ctantheta , then (x^2)/(a^2)+(y^2)/(b^2)= (a) (z^2)/(c^2) (b) 1-(z^2)/(c^2) (c) (z^2)/(c^2)-1 (d) 1+(z^2)/(c^2)

Let a ,b , c be real numbers. The following system of equations in x ,y and z (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1 has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

Let a ,b , c be the real numbers. The following system of equations in x ,y ,a n dz (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1 has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

(y^(2)+yz+z^(2))/((x-y)(x-z)) + (z^(2)+zx+x^(2))/((y-z)(y-x)) + (x^(2)+xy+y^(2))/((z-x)(z-y))