If `(a+i)^2/(2a-i)=p+iq` then prove that `p^2+q^2=((a^2+1)^2/(4a^2+1))`

Find the product: (p^2 -q^2) (2p + q)

If log((a+2b)/4)=1/2(loga+logb) ,then prove that a^2+4b^2=12ab

Of triangle ABC, angleB=90^@ and BD_|_AC .IF AB=c,BC=a,CA=b and BD=p then prove that , 1/p^2=1/a^2+1/c^2 .

If A = [(2,3),(1, 2)] prove that A^3 - 4A^2 + A = 0

Factorise : 4p^2 - 9q^2

If a, b, c are in A.P. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

Factorise the expressions : 7p^2 + 21q^2

If cos A+cos B=1/2 and sin A +sin B=1/4 then prove that tan ((A+B)/2)=1/2 .

Prove that If 3x+2y=-1 , then prove that 81x^4+16y^4+1-72x^2y^2-18x^2-8y^2=0

If A=[(2,-1),(-1,2)] , then show that A^(2) -4A +3I=O .