(1)已知a²+b²=8,a+b=4,求a-b的值(2)已知xy=3,x-y=7,求x²+y²、x+y的值

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(1)已知a²+b²=8,a+b=4,求a-b的值(2)已知xy=3,x-y=7,求x²+y²、x+y的值
(1)已知a²+b²=8,a+b=4,求a-b的值(2)已知xy=3,x-y=7,求x²+y²、x+y的值

(1)已知a²+b²=8,a+b=4,求a-b的值(2)已知xy=3,x-y=7,求x²+y²、x+y的值
(1)已知a²+b²=8,a+b=4,求a-b的值
2ab=(a+b)²-(a²+b²)=16-8=8;
(a-b)²=8-8=0;
所以a-b=0;
(2)已知xy=3,x-y=7,求x²+y²、x+y的值
x²+y²=(x-y)²+2xy
=49+6
=55;
(x+y)²=x²+y²+2xy
=55+6
=61;
所以x+y=±√61;
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(1)2ab=(a+b)²-(a²+b²)=4²-8=8
a-b=√(a-b)²=√(a²+b²-2ab)=√(8-8)=√0=0
(2)x²+y²=(x-y)²+2xy=7²+2*3=55
x+y=±√(x+y)²=±√(x²+y²+2xy)=±√(55+2*3)=±√61

(a+b)^2=16
(a+b)^2=a^2+b^2+2ab=8+2ab
2ab=16-8=8
(a-b)^2=a^2+b^2-2ab=8-2ab=0
a-b=0
(x-y)^2=49=x^2+y^2-2xy=x^2+y^2-6
x^2+y^2=49+6=55
(x+y)^2=x^2+y^2+2xy=55+6=61
x+y=±(61)^0.5