已知a,b是一元二次方程2x2-3x-1=0的两个实数根，求下列值(x1-x2)的平方 若x1、x2是一元二次方程2x^2-3x-1=0的两个根 求...
\u82e5x1,x2\u662f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b2x^2-3x+1=0\u7684\u4e24\u4e2a\u5b9e\u6839\uff0c\u6c42x1^2+x2^2\u7684\u503c\u3002x1,x2\u662f\u65b9\u7a0b\u7684\u5b9e\u6839 \u6839\u636e\u97e6\u8fbe\u5b9a\u7406 \u5219\u6709x1+x2=3/2 x1*x2=1/2
x1^2+x^2=(x1+x2)^2-2x1*x2=(3/2)^2-1=5/4
a+b=3/2
a*b=-1/2
另由
(x1-x2)^2=(a-b)^2=a^2+b^2-2a*b=(a^2+b^2+2a*b)-4a*b=(a+b)^2-4a*b
将a+b与a*b代入得
(x1-x2)^2=(3/2)*(3/2)-4*(-1/2)=9/4+2=17/4
2x^2-3x-1=0
a+b = 3/2
ab=-1/2
(a-b)^2
=(a+b)^2 - 4ab
=9/4 + 2
=17/4
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绛旓細鈭礱,b鏄竴鍏冧簩娆℃柟绋x^2-2x-1=0鐨勪袱涓疄鏁版牴 鈭碼+b锛2,ab=锕1,a²锛2a锛1锛0鍗砤²锛2a+1 鈭碼^2-5a-3b+8=2a+1-5a-3b+8锛濓梗3锛坅+b)锛9锛濓梗3脳2锛9锛3
绛旓細鈭垫牴鎹牴涓庣郴鏁扮殑鍏崇郴寰楋細a+b=2锛宎b=-1锛鈭碼 2 +b 2 =锛坅+b锛 2 -2ab=2 2 -2脳锛-1锛=6锛岋紙a-b锛 2 =a 2 +b 2 -2ab=6-2脳锛-1锛=8锛屸埓a-b=卤2 2 锛屸埓褰揳-b=2 2 鏃讹紝锛坅-b锛夛紙a+b-2锛+ab锛=2 2 脳锛2-2锛+锛-1锛=-1锛屽綋a-...
绛旓細a銆b鏄竴鍏冧簩娆℃柟绋x鐨勫钩鏂-2x-1=0鐨勪袱涓疄鏁版牴 a+b=2 ab=-1 銆恆-b銆戙恆+b-2銆+ab =(a-b)*0+ab =ab =-1
绛旓細鐢盿+b=2, ab=-1,寰:(a-b)(a+b-2)+ab =(a-b)*0-1 =-1
绛旓細a銆b鏄柟绋x²锛2x锛1=0鐨勪袱鏍癸紝鍒欙細a锛媌=2锛ab=锛1 (a锛峛)²锛峚b =a²锛3ab锛媌²=(a锛媌)²锛5ab =2²锛5脳(锛1)=9
绛旓細1)2x²+5x+3=0 x1=-1 x2=-3/2 2)(1+3x)(2x-3)=5x²-x-7 -7x+6x²-3=5x²-x-7 x²-6x+4=0 3锛夋柟绋嬶紙m²-1锛墄²+锛坢+1锛墄-1=0锛屽綋m锛堜笉绛変簬 卤1锛夋椂锛屾柟绋嬩负鍏充簬x鐨涓鍏冧簩娆℃柟绋锛涘綋m=锛 锕1锛夋椂锛屾柟绋嬩负鍏充簬x鐨勪竴鍏...
