已知实数a,b满足a+b=7,ab=12,求下列代数式的值:(1)(a-b)2(1) (a-b)² (2)a²-ab+b² (3)(a²+1)(b²+1).
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![已知实数a,b满足a+b=7,ab=12,求下列代数式的值:(1)(a-b)2(1) (a-b)² (2)a²-ab+b² (3)(a²+1)(b²+1).](/uploads/image/z/4031979-51-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3a%2Bb%3D7%2Cab%3D12%2C%E6%B1%82%E4%B8%8B%E5%88%97%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC%3A%281%29%28a-b%292%281%29+%28a-b%29%26%23178%3B+%EF%BC%882%EF%BC%89a%26%23178%3B-ab%2Bb%26%23178%3B+%EF%BC%883%EF%BC%89%EF%BC%88a%26%23178%3B%2B1%EF%BC%89%EF%BC%88b%26%23178%3B%2B1%EF%BC%89.)
已知实数a,b满足a+b=7,ab=12,求下列代数式的值:(1)(a-b)2(1) (a-b)² (2)a²-ab+b² (3)(a²+1)(b²+1).
已知实数a,b满足a+b=7,ab=12,求下列代数式的值:(1)(a-b)2
(1) (a-b)² (2)a²-ab+b² (3)(a²+1)(b²+1).
已知实数a,b满足a+b=7,ab=12,求下列代数式的值:(1)(a-b)2(1) (a-b)² (2)a²-ab+b² (3)(a²+1)(b²+1).
1) (a-b)²
=(a+b)² -4ab
=7² -4x12
=1
(2)a²-ab+b²
=(a+b)² -3ab
=7² -3x12
=49-36
=13
(3)(a²+1)(b²+1)
=a² b² +a² +b² +1
=(ab)² +(a+b)² -2ab+1
=12² +7² -2x12+1
=144+49-24+1
=170
如追加其它问题,
(a+b)^2=49=a²+2ab+b²
(a-b)²=a²+b²-2ab=49-4*12=1
a²-ab+b²=49-3*12=13
a²+1)(b²+1)=a² b² +a² +b² +1=(ab)² +(a+b)² -2ab+1=12² +7² -2x12+1=144+49-24+1=170
(1)(a-b)^2=a^2-2ab+b^2=(a^2+2ab+b^2)-4ab=(a+b)^2-4ab=49-48=1 ;
(2)a^2-ab+b^2=(a^2+2ab+b^2)-3ab=(a+b)^2-3ab=49-36=13 ;
(3)(a^2+1)(b^2+1)=(ab)^2+(a^2+b^2)+1=(ab)^2+(a^2+2ab+b^2)-2ab+1
=(ab)^2+(a+b)^2-2ab+1
=(ab-1)^2+(a+b)^2
=11^2+7^2=121+49=170 。
(1) (a-b)²=a^2+b^2-2ab=(a+b)^2-4ab=49-48=1
(2)a²-ab+b²=(a+b)^2-3ab=49-36=13
(3)(a²+1)(b²+1)=a^2b^2+a^2+b^2+1=(ab)^2+(a+b)^2-2ab+1=144+49-24+1=170