)已知X、Y、Z满足关系式：绝对值4X-4Y+1 ,+1/5根号下2Y+Z+(X-1/2)^2=0,求代数式X^2(Y-Z)的值.

题目

)已知X、Y、Z满足关系式：绝对值4X-4Y+1 ,+1/5根号下2Y+Z+(X-1/2)^2=0,求代数式X^2(Y-Z)的值.

答案

|4X-4Y+1| +1/5根号下(2Y+Z)+(X-1/2)^2=0 |4X-4Y+1|>=0 1/5根号下(2Y+Z)>=0 (X-1/2)^2>=0 4X-4Y+1=0 2Y+Z=0 X-1/2=0 X=1/2 4Y=4X+1=3 Y=3/4 Z=-2Y=-3/2 X^2(Y-Z)=(1/4)*(3/4+6/4)=9/16