若a、b是方程x²+3x-1=0的两个根,则代数式(a²+2a+1)(b²+2b+1)的值为
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![若a、b是方程x²+3x-1=0的两个根,则代数式(a²+2a+1)(b²+2b+1)的值为](/uploads/image/z/1658264-32-4.jpg?t=%E8%8B%A5a%E3%80%81b%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B%2B3x-1%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F%28a%26%23178%3B%2B2a%2B1%29%28b%26%23178%3B%2B2b%2B1%29%E7%9A%84%E5%80%BC%E4%B8%BA)
若a、b是方程x²+3x-1=0的两个根,则代数式(a²+2a+1)(b²+2b+1)的值为
若a、b是方程x²+3x-1=0的两个根,则代数式(a²+2a+1)(b²+2b+1)的值为
若a、b是方程x²+3x-1=0的两个根,则代数式(a²+2a+1)(b²+2b+1)的值为
x=a
则a²+3a-1=0
所以a²+2a+1=-a+2
同理
b²+2b+1=-b+2
a+b=-3
ab=-1
所以原式=(-a+2)(-b+2)
=ab-2(a+b)+4
=-1+6+4
=9
9
因为a、b是方程x²+3x-1=0的两个根 所以a²+2a+1=-a+2 b²+2b+1=-b+2
(a²+2a+1)(b²+2b+1) =ab-2(a+b)+4=-1-2*(-3) +4=9
a+b=-3;
ab=-1;
(a²+2a+1)(b²+2b+1)
=(a+1)²(b+1)²
=(ab+a+b+1)²
=(-1-3+1)²
=9
亲 直接变成(a+1)^2 *(b+1)^2 =(ab+a+b+1)^2
ab=-1 a+b=-3 所以答案就是9
若a、b是方程x²+3x-1=0的两个根,
a^2+3a-1=0 a^2=1-3a
b^2+3b-1=0 b^2=1-3b
(a²+2a+1)(b²+2b+1)
=(2-a)(2-b)
=4-2(a+b)+ab a+b=-3 ab=-1
=4+6-1
=9
∵a、b是方程x²+3x-1=0的两个根
∴a+b=-3 ab=-1
∴(a²+2a+1)(b²+2b+1)
=(a+1)²(b+1)²
=[(a+1)(b+1)]²
=(ab+a+b+1)²
=(-3-1+1)²
=9
a和b是方程X2+3x-1=0的根 ===》a+b= - 3,ab=1,
(a2+2a+1)(b2+2b+1)=(a+1)2(b+1)2=[ab+(a+b)+1]2=[1+(-3)+1]2=1