因式分解:已知a+b=5,ab=3,求(a²-b²)²的值

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因式分解:已知a+b=5,ab=3,求(a²-b²)²的值因式分解:已知a+b=5,ab=3,求(a²-b²)²的值因式分解:已知a+b=5

因式分解:已知a+b=5,ab=3,求(a²-b²)²的值
因式分解:已知a+b=5,ab=3,求(a²-b²)²的值

因式分解:已知a+b=5,ab=3,求(a²-b²)²的值
(a-b)²
=a²+b²-2ab
=(a+b)²-4ab
=5²-4x3
=25-12
=13
(a²-b²)²
=(a+b)²(a-b)²
=25x13
=325

a²-b²=(a+b)(a-b)=±5√13

(a-b)^2=(a+b)^2-4ab=25-12=13
(a²-b²)²
=(a+b)^2(a-b)^2
=25*13
=325

(a+b)2*(a-b)2 (a-b)2=(a+b)2-4ab=25-4*3=13 (a2-b2)2=25*13=325

(a2-b2)2=(a+b)2*(a-b)2
(a-b)2=(a+b)2-4ab=25-4*3=13
(a2-b2)2=25*13=325

(a-b)²(a+b)²=(a²+b²-4ab+2ab)×25=[(a+b)²-4ab]×25=(25-12)×25=325