# Is am-gm inequality useful here?

2 integers ( x and x+10). Find the 2 integers such that their product is at MINIMUM by using am-gm inequality.

Note by William Isoroku
2 years, 4 months ago

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I prefer not to approach this question with AM-GM Inequality. Let $$y = x(x+10)$$, we can write it into the form of $$y = (x+5)^2-25$$. Here, the value $$x$$ such that $$y$$ is a minimum is $$x = -5$$ and $$y = -25$$. The two integers is then -5 and 5.

- 2 years, 4 months ago