If `y=x+1/x` then `x^4+x^3-4x^2+x+1=0` becomes

If y=(x+(1)/(x)) , then the expression x^(4) +x^(3) -4x^(2) +x +1=0 can be simplified in terms of y as

If 2x-1/(3x)=y then 9x^2+1/(4x^2) in terms of y is

Q. the equation of image of the pair of lines y=|2x-1| in y-axis is (A) 4x^2-y^2-4x+1=0 (B) 4x^2-y^2+4x+1=0 (C) 4x^2+y^2+4x+1=0 (D) 4x^2+y^2-4x+1=0

If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value of |[x^3-1, 0, x-x^4], [0, x-x^4, x^3-1], [x-x^4, x^3-1, 0]|

If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value of |[x^3-1, 0, x-x^4], [0, x-x^4, x^3-1], [x-x^4, x^3-1, 0]|

If the circle x^2 + y^2 = a^2 intersects the hyperbola xy=c^2 in four points P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4) , then : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^4x^3-1x-x^4x^3-1 0|

If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^4x^3-1x-x^4x^3-1 0|

If y = tan ^(-1) ((2x )/( 1 -x ^(2))) + tan ^(-1) ((3x - x ^(3))/( 1 - 3x ^(2)))- tan ^(-1) ((4x - 4x ^(3))/( 1 - 6x + x ^(4))), then show that (dy)/(dx) = (1)/(1 + x ^(2)).