The vertices of a triangle are `(p q ,1/(p q)),(q r ,1/(q r)),` and `(r p ,1/(r p)),` where `p ,q` and `r` are the roots of the equation `y^3-3y^2+6y+1=0` . The coordinates of its centroid are

The base vertices of an isosceles triangle PQR are Q (1,3) and R(-2, 7). The vertex P can be-

Show that the points (p , q , r) , (q , r , p) and (r , p , q) are the vertices of an equilateral triangle.

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

If the roots of the equation (x - p) (x - q) -r = 0 are alpha , beta then the roots of the equation (y - beta) (y - alpha) + r = 0 are

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show that 1/p+1/r=2/q .

The vertices of Delta PQR " are " P (2, 1) , Q (-2, 3) " and " R (4, 5) . Find equation of the median through the vertex R.

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are

Prove that the area of the triangle with vertices (p,q),(x_(1),y_(1)) and (x_(2),y_(2)) where p,x_(1),x_(2) are in G.P. with common ratio r_(1) and q, y_(1), y_(2) and in G.P with common ratio r_(2) is (1)/(2) pq(r_(1)-1) (r_(2)-1) (r_(2)-r_(1)) sq unit.

If p,q and r are simple propositions such that (p^^q)^^(q^^r) is true, then