Question

已知(x+y)²=5,(x-y)²=3,求3xy-1的值

Answer 1

(x+y)²=5
x²+y²+2xy=5①
(x-y)²=3
x²+y²-2xy=3②
①-②
4xy=2
xy=1/2
3xy-1
=3/2-1
=1/2
x²+y²-6x+4y+13=0
(x²-6x+9)+(y²+4y+4)=0
(x-3)²+(y+2)²=0
x=3
y=-2
x^y
=3^(-2)
=1/9
若a(a-1)-(a²-b)=5,求(a²+b²)/2-ab
a²-a-a²+b=5
b-a=5
b=5+a
(a²+b²)/2-ab
=[a²+(5+a)²]/2-a(5+a)
=(a²+25+10a+a²)/2-5a-a²
=(2a²+10a+25)/2-5a-a²
=a²+5a+25/2-5a-a²
=25/2
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