((x^(-4))/(y^(-10)))^(5/4)

Show that: (x^(2)+y^(2))^(5)=(x^(5)-10x^(3)y^(2)+5xy^(4))^(2)+(5x^(4)-10x^(2)y^(3)+y^(5))^(2)

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

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

In a cyclic quadrilateral ABCD ,/_A=(2x+4)^(@),/_B=(x+10)^(@),/_C=(4y-4) and /_D=(5y+5)^(@). Find the values of x and y hence find all the angles.

The length of the major axis of the ellipse (5x-10)^(2)+(5y+13)^(2)=((3x-4y+7)^(2))/(4) is

Differentiate w.r.t x, y y = (4x^(2) - 5x + 10)^(10)

(10)/(x+y)+(2)/(x-y)=4,(15)/(x+y)-(5)/(x-y)=-2

Verify that (x+y)xxz=x xxz+yxxz , if (i) x=(4)/(5), y=(-2)/(3) "and" z=-4 (ii) x=2, y=(4)/(5) "and" z=(3)/(-10)