若实数x,y满足x²+y²=2x,求x²-y²的取值范答案是﹣0.5小于等于x²-y²小于等于4
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若实数x,y满足x²+y²=2x,求x²-y²的取值范答案是﹣0.5小于等于x²-y²小于等于4
若实数x,y满足x²+y²=2x,求x²-y²的取值范
答案是﹣0.5小于等于x²-y²小于等于4
若实数x,y满足x²+y²=2x,求x²-y²的取值范答案是﹣0.5小于等于x²-y²小于等于4
2x-x²=y²>=0
x²-2x
x²+y²=2x
x²-2x+y²=0
x²-2x+1+y²=1
(x-1)²+y²=1
令x=1+cosa,y=sina
x²-y²=(1+cosa)²-sin²a
=cos²a+2cosa+1-sin...
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x²+y²=2x
x²-2x+y²=0
x²-2x+1+y²=1
(x-1)²+y²=1
令x=1+cosa,y=sina
x²-y²=(1+cosa)²-sin²a
=cos²a+2cosa+1-sin²a
=cos²a+2cosa+1-(1-cos²a)
=2cos²a+2cosa
=2(cosa +1/2)² -1/2
-1≤cosa≤1 0≤(cosa+1/2)²≤9/4
-1/2≤2(cosa+ 1/2)²≤4
-1/2≤x²-y²≤4
x²-y²的取值范围为[-1/2,4]。
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