已知:a+b=5,ab=3求a²-b²的值

已知:a+b=5,ab=3求a²-b²的值
已知:a+b=5,ab=3求a²-b²的值

已知:a+b=5,ab=3求a²-b²的值
(a-b)²=a²-2ab+b²=a²+2ab+b²-4ab=(a+b)²-4ab=25-12=13
∴a-b=±√13
∴a²-b²
=(a+b)(a-b)
=±5√13

a^2-b^2=(a+b)(a-b)
=3*5=15

a+b)2= 25
a2+b2+2ab=25
a2+b2=19
a-b)2
=a2+b2-2ab
=19-6
=11
∴a-b=±√13
∴a²-b²
=(a+b)(a-b)
=±5√13
采纳，呵呵