[+-(1)/(sqrt(p^(2)+q^(2))-sqrt(p^(2)-q^(2)))<=m+ar],[q^(2)x^(2)-2p^(2)x+q^(2)=0]

if x=(sqrt(p^(2)+q^(2))+sqrt(p^(2)-q^(2)))/(sqrt(p^(2)+q^(2))-sqrt(p^(2)-q^(2))), then q^(2)x^(2)-2p^(2)x+q^(2)=?

If x=(sqrt(p^(6)+q^(2))+sqrt(p^(2)-q^(2)))/(sqrt(p^(2)+q^(2))-sqrt(p^(2)-q^(2))) then q^(2)x^(2)-2p^(2)x+q^(2)=?

If AM and GM of x and y are in the ratio p: q, then x: y is : a) p - sqrt(p^(2)+ q^(2)) : p +sqrt (p^(2)+ q^(2)) b) p +sqrt(p^(2) - q^ (2) ) : p- sqrt(p^(2)-q^(2)) c) p : q d) p + sqrt(p^(2) + q^(2)) : p-sqrt(p^(2) + q^(2))

lim_(x rarr0)(sqrt(4^(2)+p^(2))-p)/(sqrt(x^(2)-q^(2)-q))

If the ratio of A.M. of two numbers x and y to their G.M. is p : q, show that, x : y = (p + sqrt(p^(2) - q^(2))) : (p- sqrt(p^(2) - q^(2)))

lim_(x rarr0)(sqrt(x^(2)+q^(2))-q)/(sqrt(x^(2)+p^(2))-p)

Prove that the equation p cos x - q sin x =r admits solution for x only if -sqrt(p^(2)+q^(2)) lt r lt sqrt(p^(2)+q^(2))

Prove that the equation p cos x - q sin x =r admits solution for x only if -sqrt(p^(2)+q^(2)) lt r lt sqrt(p^(2)+q^(2))

Prove that the equation p cos x - q sin x =r admits solutin for x only if -sqrt(p^(2)+q^(2)) lt r lt sqrt(p^(2)+q^(2))

x=(sqrt(p^2+q^2)+sqrt(p^2-q^2))/(sqrt(p^2+q^2)-sqrt(p^2-q^2)) then q^2x^2-2p^2x+q^2=? (A)    3    (B)    -1    (C)    -2    (D)    0