The square root of the complex number `z =(u^(2))/(v^(2))+(v^(2))/(u^(2))+(1)/(2i)((u)/(v)+(v)/(u))+(31)/(16)` is

int(vdu-udv)/(u^(2)+v^(2))=

int(udu+vdv)/(u^(2)+v^(2))=

int_(1)^(2)((x^(2)-1)dx)/(x^(3)*sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where u are ( in their blowest form.Find the value of )/(sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where of ((1000)u)/(v)

The function u=e^(x)sin x,v=e^(x)cos x satisfy the equation (a) v(du)/(dx)-u(du)/(dx)=u^(2)+v^(2)(b)(d^(2)u)/(dx^(2))=2v(c)d^(2)v())/(dx^(2))=-2u(d)(du)/(dx)+(dv)/(dx)=2v

Solve the following system of equations: (15)/(u)+(2)/(v)=17,quad (1)/(u)+(1)/(v)=(36)/(5)

Find the value of (-8u^(2)v^(6))xx(-20uv) for u=2.5 and v=1

Test the dimensional consistency of the following equations : (i)v=u+at" "(ii) v^(2)=u^(2)+2as" "(iii)E=mc^(2)" "(iv)(1)/(2)mv^(2)=mgh

Let a,b,c,d be real numbers in G.P. If u,v,w satisfy the system of equations u+2y+3w=6,4u+5v+6w=12 and 6u+9v=4 then show that the roots of the equation ((1)/(u)+(1)/(v)(+)/(w))x^(2)+[(b-c)^(2)+(c-a)^(2)+(d-b)^(2)]x+u+v+w=0 and 20x^^2+10(a-d)^^2x-9=0 ' are reciprocals of each other.