`costheta=(a^(2)+b^(2))/(2ab)`, where a and b are two distinct numbers such that `ab gt 0`.

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

If 9a^(2)-6ab+b^(2)=0 then find a:b

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

The number ab - ba where a and b are digits and a gt b is divisible by ________.

If a,b,c are three distinct positive real numbers in G.P., than prove that c^2+2ab gt 3ac .

If a,b,c are three distinct positive real numbers in G.P., than prove that c^2+2ab gt 3ac .

Between two distinct rational numbers a and b there exists another rational numbers which is (a)/(2)( b) (b)/(2)(c)(ab)/(2) (d) (a+b)/(2)