If `x+1/x=p` then show that `x^3+1/x^3=p^3-3p`

If x+(1)/(x)=p, the value of x^(3)+(1)/(x^(3)) is p^(3)+(1)/(p^(3))(b)p^(3)-3p(c)p^(3)(d)p^(3)+3p

Let- 1<=p<1 show that the equation 4x^(3)-3x-p=0 has a unique root in the interval [(1)/(2),1]

If p(4)=3x^(2)+2x-2, then the value of p(3)-p(-1)+p((1)/(2)) is

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))

If p = x^(1//3) + x^(-1//3), then p^3 - 3p is equal to :

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If X has a poisson distribution such that P(x=2)=(2)/(3)P(x=1) then P(x=3) is

If each pair ofthe following three equations x: x^(2)+p_(1)x+q_(1)=0.x^(2)+p_(2)x+q_(2)=0x^(2)+p_(3)x+q_(3)=0, has exactly one root common, prove that (p_(1)+p_(2)+p_(3))^(2)=4(p_(1)p_(2)+p_(2)p_(3)+p_(3)p_(1)-q_(1)-q_(2)-q_(3)]

Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=1/3. Then