If `a + (1)/(a)= p and a ne 0`, then show that: `a^(3) + (1)/(a^(3))= p (p^(2)- 3)`

If (a + (1)/(a))^(2) = 3 and a ne 0 , then show that: a^(3) + (1)/(a^(3))= 0

If A=((p,q),(0,1)) , then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(0,1))

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

Let A, B and C be three mutually exclusive events such that P(A) = p_(1) , P(B) = p_(2) and P( C) = p_(3) . Then, Let p_(1) = 1/2(1-p), p_(2) = 1/3(1+2p) " and " p_(3) = 1/5(2+3p) , then p belongs to

Let A, B and C be three mutually exclusive events such that P(A) = p_(1), P(B) = p_(2) " and " P( C) = p_(3) . Then, Let p_(1) = 1/3(1+3p), p_(2) = 1/4(1-p) " and " p_(3) = 1/4(1-2p) , then p belongs to

If p + 1/( p + 2 ) = 3 , find the value of ( p + 2 )^3 + 1/( p + 2 )^3

If p_(1),p_(2),p_(3) are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))

Let the lengths of the altitudes from the vertices A(-1, 1), B(5, 2), C(3, -1) of DeltaABC are p_(1), p_(2), p_(3) units respectively then the value of (((1)/(p_(1)))^(2)+((1)/(p_(3)))^(2))/(((1)/(p_(2)))^(2)) is equal to

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 A =[{:(0,1,0),(0,0,1),(p,q,r):}] , show that ltbargt A^(3)= pI+qA+rA^(2)