If b is the mean proportion between a and c, show that :
`(a^(4)+a^(2)b^(2)+b^(4))/(b^(4)+b^(2)c^(2)+c^(4))=a^(2)/c^(2)`

(i) If a , b , c are in continued proportion, show that : (a^(2) + b^(2))/(b(a+c)) = (b(a + c))/(b^(2) + c^(2)) . (ii) If a , b , c are in continued proportion and a(b - c) = 2b , prove that : a - c = (2(a + b))/(a) . (iii) If (a)/(b) = (c)/(d) show that : (a^(3)c + ac^(3))/(b^(3)d +bd^(3)) = ((a + c)^(4))/((b + d)^(4)) .

If a, b, c are in continued proportion, prove that (a+b+c)(a-b+c)=a^(2)+b^(2)+c^(2) .

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

Factorise : 4a^(2) - (4b^(2) + 4bc + c^(2))

The value of c for which the equation a x^2+2b x+c=0 has equal roots is (a) (b^2)/a (b) (b^2)/(4a) (c) (a^2)/b (d) (a^2)/(4b)

Which of the following is equivalent to (2b^(3)c^(2)+b^(2)c)-(b^(3)c^(2)-b^(2)c-4bc) ?

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

If a,b,c are non-zero real numbers, then the minimum value of the expression ((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2)) equals

If a x^2+b x+c=0 has equal roots, then c= (a) b/(2a) (b) b/(2a) (c) (-b^2)/(4a) (d) (b^2)/(4a)

if alpha , beta are root of ax^2+bx+c=0 then (1/alpha^2+1/beta^2)^2 (a) (b^(2)(b^(2)-4ac))/(c^(2)a^(2)) (b) (b^(2)(b^(2)-4ac))/(ca^(3)) (c) (b^(2)(b^(2)-4ac))/(a^(4)) (d) (b^(2)-2ac)^2/(c^(4))