x²+ab/根下【a²b²+(a²+b²)x²+x^4】用均值不等式解,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 15:09:42
![x²+ab/根下【a²b²+(a²+b²)x²+x^4】用均值不等式解,](/uploads/image/z/8511571-19-1.jpg?t=x%26%23178%3B%2Bab%2F%E6%A0%B9%E4%B8%8B%E3%80%90a%26%23178%3Bb%26%23178%3B%2B%28a%26%23178%3B%2Bb%26%23178%3B%29x%26%23178%3B%2Bx%5E4%E3%80%91%E7%94%A8%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%A7%A3%2C)
x²+ab/根下【a²b²+(a²+b²)x²+x^4】用均值不等式解,
x²+ab/根下【a²b²+(a²+b²)x²+x^4】用均值不等式解,
x²+ab/根下【a²b²+(a²+b²)x²+x^4】用均值不等式解,
a²+b²≥2ab
∴a²b²+(a²+b²)x²+x^4≥a²b²+2abx²+x^4=(x²+ab)²
∴x²+ab/根下{a²b²+(a²+b²)x²+x^4}≥x²+ab/根下(x²+ab)²
当x²+ab>0时,结果≥1
当x²+ab