" 38.If "a^(x)=b^(y)=c^(z)" and "a^(3)=b^(2)c" ,then "(3)/(x)-(2)/(y)=

If a^(x)=b^(y)=a^(z) and a^(3)=b^(2)c, then (3)/(x)-(2)/(y)=

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

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

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

If a ,\ b ,\ c >0\ a n d\ 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- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

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+b+z)^(2)+(a+b+c)^(2))

If a, b, c, x, y and z be real numbers and x^(2)+y^(2)+z^(2)=16 , a^(2)+b^(2)+c^(2)=9 and ax+by+cz=12 ; the value of ((a^(3)+b^(3)+c^(3))^((1)/(3)))/((x^(3)+y^(3)+z^(3))^((1)/(3))) is