a+b=3 ab=-12①求a^2 +b^2②求(a-b)^2已知x-2y=15 xy=-25 求x^2 +4y^2-1已知x-y=5 (x+y)^2=49 求x^2 +y^2
问题描述：
a+b=3 ab=-12
①求a^2 +b^2
②求(a-b)^2
已知x-2y=15 xy=-25 求x^2 +4y^2-1
已知x-y=5 (x+y)^2=49 求x^2 +y^2
答
a^2 +b^2=(a+b)^2-2ab=3^2+2*12=33;
(a-b)^2=(a+b)^2-4ab=3^2+4*12=57;
x^2 +4y^2-1=(x-2y)^2+4xy-1=15^2-4*25-1;
x^2 +y^2 =1/2[(x+y)^2+(x-y)^2]=1/2(49+25) .
答
1) a^2+b^2=(a+b)^2-2ab=3^2-(-12)*2=33
2) (a-b)^2=a^2+b^2-2ab=33-2*(-12)=57
x^2 +4y^2-1 =(x-2y)^2+4xy-1=15^2-4*25-1=124
4xy=(x+y)^2-(x-y)^2=24
2xy=12
x^2+y^2=(x+y)^2-2xy=49-12=37
答
a^2+b^2=(a+b)^2-4ab=9-(-24)=33 (a-b)^2 =a^2+b^2-2ab=33+24=57 x^2 +4y^2-1=(x-2Y)^2-4xy-1=225+100-1=324 x-y=5 (x+y)^2=49 求x^2 +y^2 x^2 +y^2 =(x+y)^2+(x-y)^2/2=37
答
a^2 +b^2=(a+b)^2-2ab=33
(a-b)^2=(a+b)^2-4ab=57
x^2 +4y^2-1=(x-2y)^2+4xy-1=624-20/3
x^2 +y^2=((x-y)^2+(x+y)^2)/2=37