(ii) `x^(b-c)timesx^(c-a)timesx^(a-b)=`

If a, b, c are rational and no two of them are equal, then the equations (b-c)x^(2)+(c-a)x+(a-b)=0 and, a(b-c)x^(2)+ b(c-a)x+c(a-b)=0

If a, b, c are in H.P., then the equation a(b-c) x^(2) + b(c-a)x+c(a-b)=0

If a, b and c are in AP and if the equations (b-c)x^2 + (c -a)x+(a-b)=0 and 2 (c +a)x^2+(b +c)x+(a-b)=0 have a common root, then

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

Show that : (i) x^(a(b-c))/(x^(b(a-c)))/((x^b)/(x^a))^c=1 , (ii) ((x^(a+b))^2(x^(b+c))^2(x^(c+a))^2)/((x^a x^b x^c)^4)=1

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

If b is the harmonic mean of a and c and alpha, beta are the roots of the equation a(b-c)x^(2) + b(c-a) x+ c(a-b)=0 , then

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.