Question

1.已知(x+y)的平方=9,(x-y)的平方=5,求x方+y方的值

Answer 1

X^2+2XY+Y^2=9,X^2-2XY+Y^2=5两式子相加,得到2X^2+2Y^2=14,X^2+Y^2=7

X^2-10X+Y^2+4Y+29=X^2-10X+25+Y^2+4Y+4=(X-5)^2+(Y+2)^2=0推出(X-5)^2=0,(Y+2)^2=0得X=5,Y=-2,得到X^-2-Y=(1/X^2)-7=1/25+2=51/25