Quantative aptitude problems

SUB DUPLICATE OF X = ROOT X

THEREFORE, X^2= ROOT X^2 = X

B). 2S/3T = (2S-P)^2/(3T-P)^2 AFTER SOLUTION THEN

ANSWER IS (9T^2-6TP+P^2)2S = (4S^2-4SP+P^2)3T

subduplicate ratio of a:b is root(a):root(b)

implies root(P-X2):root(Q-x2) = P:Q

squaring on both sides we ger (P-X2)/(Q-X2) = P^2/Q^2

SOLVING FOR X2 GIVES X2 AS P*Q/(P+Q)

duplicate ratio of a:b is a^2:b^2

2S/3T = (2S-P)^2/(3T-P)^2

NOW TAKING ROOT ON BOTH SIDES ( WE NEED TO FIND P WHICH WOULD BE RATHER MESSY IF DONE IN QUADRATIC )

ROOT(2S)/ROOT(3T) = (2S-P)/(3T-P)

SOLVING FOR P GIVES P AS -ROOT(2S)*ROOT(3T)