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`

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 (a)/(x-a) + (b)/(y-b) + (c )/(z-c)=2 find (x)/(x-a) + (y)/(y-b) + (z)/(z-c) = ?

If (x)/(b+c-a)=(y)/(c+a-b)=(z)/(a+b-c) show that (b-c)x+(c-a)y+(a-b)z=0

If (a+b)/(x)=(b+c)/(y)=(c+a)/(z), then (A) (a+b+c)/(x+y+z)=(ab+bc+ca)/(ay+bz+cx)(B)(c)/(y+z-x)=(a)/(x+z-y)=(b)/(x+y-z)(C)(c)/(x)=(a)/(y)=(b)/(z)(D)(a+b)/(b+c)=(a+b+x)/(b+c+y)

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]|

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)

(log a)/(y-z)=(log b)/(z-x)=(log c)/(x-y), thena ^(x)b^(y)c^(z) is

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