Question

初二解方程组题目一道——————————————————————————

(x+y)²-3(x+y)-10=0
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x²-8xy+16y²=25

Answer 1

(x+y)²-3(x+y)-10=0①
｛
x²-8xy+16y²=25②
由①得（x+y-5)(x+y+2)=0
x+y-5=0或 x+y+2=0
由②得（x-4y)²=25
x-4y=±5
可组合得x+y-5=0① x+y-5=0② x+y+2=0③ x+y+2=0④
x-4y= 5 x-4y=-5 x-4y=+5 x-4y=-5
解方程组①②③④得原方程组解为
x1=5 x2=3 x3=-3/5 x4=-13/5
y1=0 y2=2 y3=-7/5 y4=3/5

x-4y=5

Answer 2

x²-8xy+16y²=25------(X-4Y)²=25-----X=4Y+5
将X=4Y+5带入(x+y)²-3(x+y)-10=0----------Y*（24Y+35)=0
Y=0或24Y+35=0
得出Y=0 X=5 或 Y=-35/24 X=-0.83333

Answer 3

(x-4y)²=25~~~x=4y+-5
将x带入（x+y)²-3(x+y)-10=0中，
得：（4y+y+-5）²-3(4y+-5+y)-10=0
（5y+-5）²-3(5y+-5)-10=0

Answer 4

（x+y-5）(x+y+2)=0
(x-4y)²=25
得x1=5,y1=0
x2=3,y2=2
x3=-3/5,y3=-7/5
x4=-13/5,y4=3/5