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November 7th, 2016, 12:23 AM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  exponential inequality
Consider the inequality $9^xa\cdot 3^xa+3\leq 0,$ where $a$ is a real parameter. Find the value of $a$ so that $(1)$ The inequality has at least one negative solution $(2)$ The inequality has at least one positive solution Last edited by skipjack; November 7th, 2016 at 12:52 AM. 
November 7th, 2016, 09:23 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,370 Thanks: 1274 
write $u=3^x$ and solve the resulting quadratic. $3^x$ is monotonic increasing in $x$ so you can then solve for $x$ from $u$ and the inequalities remain unchanged. 

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exponential, inequality 
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