If p, q are the roots of the quadratic equation x2 + 2bx + c = 0,
prove that 2log (√(y – p) + √(y – q)) = log2 + log(y + b + √(y2 + 2by + c))

Let x_(1),x_(2) are the roots of the quadratic equation x^(2) + ax + b=0 , where a,b, are complex numbers and y_(1), y_(2) are the roots of the quadratic equation y^(2) + |a|yy+ |b| = 0 . If |x_(1)| = |x_(2)|=1 , then prove that |y_(1)| = |y_(2)| =1

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

If y log x= x-y , prove that (dy)/(dx)= (log x)/((1+log x)^(2))

For relation 2 log y - log x - log ( y-1) =0

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. none of these

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If y=a^(x^(a^x..oo)) then prove that dy/dx=(y^2 log y )/(x(1-y log x log y))

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

Solve for x and y, if x gt 0 and y gt 0 : log xy = "log" (x)/(y) + 2 log 2 = 2 .

If p = log 20 and q = log 25, find the value of x, if 2 log(x + 1) = 2p - q.