解方程组:①x²+y²=5.②2x²-5xy-3y²=0 解方程:(x/x+2)
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解方程组:①x²+y²=5.②2x²-5xy-3y²=0 解方程:(x/x+2)²-1/2(x/x+2)=3
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【第一题】解方程组:
①x²+y²=5.
②2x²-5xy-3y²=0
由②得,(x-3y)(2x+y)=0
解得,x = 3y 或 x = - y/2
把x=3y代入①得,
(3y)²+y² = 5
解得,y1 = (√2)/2,y2 = - (√2)/2
∴ x1 = 3(√2)/2,x2 = - 3(√2)/2
再把 x = - y/2 代入①得,
(- y/2)²+y² = 5
解得,y3 = 2,y4 = - 2
∴ x3= - 1,x4= 1
综上所述,原方程组的解为
x1 = 3(√2)/2,y1 = (√2)/2 或 x2 = - 3(√2)/2,y2 = - (√2)/2
或 x3= - 1,y3 = 2 或 x4= 1,y4 = - 2
【第二题】
解方程:[ x/(x+2) ]² - (1/2)*[x /(x+2) ] = 3
令 u = x/(x+2),
即 x =2u /(1-u)…………………………………………(*)
则,原方程转化为
2u² - u - 6 = 0
解得,
u1= 2,u2 = - 3/2
把u1= 2 代入(*)式,解得 x1= - 4
把u2 = - 3/2 代入(*)式,解得 x2= - 6/5
综上所述,原方程的解为 x= - 4 或 x = - 6/5
①x²+y²=5.
②2x²-5xy-3y²=0
由②得,(x-3y)(2x+y)=0
解得,x = 3y 或 x = - y/2
把x=3y代入①得,
(3y)²+y² = 5
解得,y1 = (√2)/2,y2 = - (√2)/2
∴ x1 = 3(√2)/2,x2 = - 3(√2)/2
再把 x = - y/2 代入①得,
(- y/2)²+y² = 5
解得,y3 = 2,y4 = - 2
∴ x3= - 1,x4= 1
综上所述,原方程组的解为
x1 = 3(√2)/2,y1 = (√2)/2 或 x2 = - 3(√2)/2,y2 = - (√2)/2
或 x3= - 1,y3 = 2 或 x4= 1,y4 = - 2
【第二题】
解方程:[ x/(x+2) ]² - (1/2)*[x /(x+2) ] = 3
令 u = x/(x+2),
即 x =2u /(1-u)…………………………………………(*)
则,原方程转化为
2u² - u - 6 = 0
解得,
u1= 2,u2 = - 3/2
把u1= 2 代入(*)式,解得 x1= - 4
把u2 = - 3/2 代入(*)式,解得 x2= - 6/5
综上所述,原方程的解为 x= - 4 或 x = - 6/5
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