If `(y^2-5y+3)(x ^2+x+1)<2x` for all `x in R ,` then find the interval in which `y` lies.

If (3x-5y)/(3x+5y) = 1/2 . Then find the value of (3x^(2)-5y^(2))/(3x^(2) + 5y^(2)) .

If (3x-5y)/(3x+5y)=1/2 find the value of (3x^2-5y^2)/(3x^2+5y^2)

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

If x=(sqrt3+1)/(sqrt3-1) and xy=1 then find the value of (3x^2+5xy+3y^2)/(3x^2-5xy+3y^2)

Draw graph of y=(x^(3)-5x)/(x^(2)+1) .

Simplify : (2x+y)^(5)-5y(2x+y)^(4)+10y^(2)(2x+y)^(3)-10y^(3)(2x+y)^(2)+5y^(4)(2x+y)-y^(5)

A triangle has vertices A_i(x_i , y_i)fori=1,2,3 If the orthocentre of triangle is (0,0), then prove that |x_2-x_3 y_2-y_3 y_1(y_2-y_3)+x_1(x_2-x_3) x_3-x_1y_2-y_3y_2(y_3-y_1)+x_1(x_3-x_1) x_1-x_2y_2-y_3y_3(y_1-y_2)+x_1(x_1-x_2)|=0

If x= (sqrt5+1)/(sqrt5-1) and x = 1/y then find the value of (3x^(2) -7xy + 3y^(2))

Answer any One question : If (3x - 2y) : (x + 3y) = 5 : 6, then find the value of (2x + 5y) : (3x + 4y).

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)