" 14."x" in fere "5 pi" wifer? ":4x^(2)-4a^(2)x+a^(2)-b^(4)=0

4 (2x-3) ^ (2) - (2x-3) -14 = 0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Prove that sinfrac {pi}{14} is a root of the equation 8x^(3) -4x^(2) - 4x +1 = 0 .

The biquadratic equation, two of whose roots are 1+i , 1-sqrt(2) is A) x^(4)-4x^(3)+5x^(2)-2x-2=0 B) x^(4)-4x^(3)-5x^(2)+2x+2=0 C) x^(4)+4x^(3)-5x^(2)+2x-2=0 D) x^(4)+4x^(3)+5x^(2)-2x+2=0

From the points (3,4), chords are drawn to the circle x^(2)+y^(2)-4x=0 .The locus of the midpoints of the chords is (a) x^(2)+y^(2)-5x-4y+6=0(b)x^(2)+y^(2)+5x-4y+6=0(c)x^(2)+y^(2)-5x+4y+6=0(d)x^(2)+y^(2)-5x-4y-6=0

Find each of the products: (-(2)/(7)a^(4))x(-(3)/(4)a^(2)b)x(-(14)/(5)b^(2))

let cos((pi)/(7)),cos((3 pi)/(7)),cos((5 pi)/(7)), the roots of equation 8x^(3)-4x^(2)-4x+1=0 then the value of sin((pi)/(14)),sin((3 pi)/(14)),sin((5 pi)/(14))

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))