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November 7th, 2016, 12:23 AM   #1
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exponential inequality

Consider the inequality $9^x-a\cdot 3^x-a+3\leq 0,$ 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.
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November 7th, 2016, 09:23 AM   #2
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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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