Show that the solutions of the equation `[x y z t]^2=Oa r e[x y z t]=[+-sqrt(alphabeta)-betaalpha+-sqrt(alphabeta)],w h e r ealpha,beta` are libitrary.

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.

Find the number of solutions of the equation x + y + z = 6, where x, y, z, in W.

The number of integers solutions for the equation x+y+z+t=20 , where x,y,z t are all ge-1 , is

If y=sqrt((t-alpha)/(beta-t)) and x=sqrt((t-alpha)(beta-t)) then find (dy)/(dx)

If the system of equations x+ y + z = 5 , x+2y+3z=9, x+3y+alphaz=beta has unique solution, then value of alpha can’t be:

The number of integral solutions of equation x+y+z+t=29, when x>=1,y>=2,z>=2,3 and t>=0 is

If the system of linear equations {:(2x+y-z=3),(x-y-z=alpha),(3x+33y-betaz=3):} has infinitely many solution, then alpha+beta-alphabeta is equal to ______.

The three angular points of a triangle are given by Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma are complex numbers, then prove that the perpendicular from the angular point Z=alpha to the opposite side is given by the equation R e((Z-alpha)/(beta-gamma))=0

The equation x = (e ^(t) + e ^(-t))/(2), y = (e ^(t) -e^(-t))/(2), t in R, represents