If `x^(a)=c^(b)` and `x^(c)=c^(a)` then prove that `a^(2)=bc`

If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b^2+bc+c^2).y^(c^2+ca+a^2).z^(a^2+ab+b^2)=1

If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are equal, prove that 2a=b+c .

If ax+by+c=0 " and " a'x+b'y+c'=0 , then prove that x/(bc'-b'c)=y/(ca'-c'a)=1/(ab'-a'b)

AD is the perpendicular from A and BC of triangleABC .If AB=c,BC=a,CA=b and AD=x then prove that a=sqrt(b^2-x^2)+sqrt(c^2-x^2)

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c .

If the roots of the equations (b-c) x^(2) + (c-a) x+( a-b) =0 are equal , then prove that 2b=a+c

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c