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$a + b = p ; ab = -1 $$c + d = -q ; cd = 1 $$VT = (a^2 - ad - ac + cd).(b^2 - bc - bd + cd) = [ a^2 - a(c + d) +1 ].[ b^2 -b(c + d) +1 ] $$= ( a^2 + aq + 1).( b^2 + bq + 1) = (ab)^2 + a^2bq + a^2 + ab^2q + abq^2 + aq + b^2 + bq +1 $$= 2 + a^2bq + ab^2q + abq^2 + (a+b)^2 - 2ab + q(a+b) $$= 2 - aq - bq - q^2 + p^2 +2 + pq $$= 4 - q(a+b) + p^2 - q^2 + pq $$= 4 - pq + p^2 - q^2 + pq $$= p^2 - q^2 +4$(đpcm)

$a + b = -p ; ab = 1 $$c + d = -q ; cd = 1 $$VT = (a^2 - ad - ac + cd).(b^2 - bc - bd + cd) = [ a^2 - a(c + d) +1 ].[ b^2 -b(c + d) +1 ] $$= ( a^2 + aq + 1).( b^2 + bq + 1) = (ab)^2 + a^2bq + a^2 + ab^2q + abq^2 + aq + b^2 + bq +1 $$= 2 + a^2bq + ab^2q + abq^2 + (a+b)^2 - 2ab + q(a+b) $$= 2 - aq - bq - q^2 + p^2 +2 + pq $$= 4 - q(a+b) + p^2 - q^2 + pq $$= 4 - pq + p^2 - q^2 + pq $$= p^2 - q^2 +4$(đpcm)

a + b = p ; ab = -1 c + d = -q ; cd = 1 VT = (a^2 - ad - ac + cd).(b^2 - bc - bd + cd) = [ a^2 - a(c + d) +1 ].[ b^2 -b(c + d) +1 ] = ( a^2 + aq + 1).( b^2 + bq + 1) = (ab)^2 + a^2bq + a^2 + ab^2q + abq^2 + aq + b^2 + bq +1 = 2 + a^2bq + ab^2q + abq^2 + (a+b)^2 - 2ab + q(a+b) = 2 - aq - bq - q^2 + p^2 +2 + pq = 4 - q(a+b) + p^2 - q^2 + pq = 4 - pq + p^2 - q^2 + pq = p^2 - q^2 +4(đpcm)

$a + b = p ; ab = -1 $$c + d = -q ; cd = 1 $$VT = (a^2 - ad - ac + cd).(b^2 - bc - bd + cd) = [ a^2 - a(c + d) +1 ].[ b^2 -b(c + d) +1 ] $$= ( a^2 + aq + 1).( b^2 + bq + 1) = (ab)^2 + a^2bq + a^2 + ab^2q + abq^2 + aq + b^2 + bq +1 $$= 2 + a^2bq + ab^2q + abq^2 + (a+b)^2 - 2ab + q(a+b) $$= 2 - aq - bq - q^2 + p^2 +2 + pq $$= 4 - q(a+b) + p^2 - q^2 + pq $$= 4 - pq + p^2 - q^2 + pq $$= p^2 - q^2 +4$(đpcm)