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 panky November 7th, 2016 12:23 AM

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

 romsek November 7th, 2016 09:23 AM

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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