log _1/4( 35 x^2x #10;) ≥ 12 #10; #10; 35 x^2x≤( 14)^ #10;12 #10; #10; 35 x^2x≤( 4 )^1/2 #10; #10; 35 x^2x≤ 2 ...

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Standard Limits to Remove Indeterminate Form

log1/435-x2x≥...

Question

${log}_{1 / 4} (\frac{35 - x^{2}}{x}) \geq - \frac{1}{2}$

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Solution

${log}_{1 / 4} (\frac{35 - x^{2}}{x}) \geq \frac{- 1}{2}$

$\frac{35 - x^{2}}{x} \leq {(\frac{1}{4})}^{\frac{- 1}{2}}$

$\frac{35 - x^{2}}{x} \leq {(4)}^{1 / 2}$

$\frac{35 - x^{2}}{x} \leq 2$

$35 - x^{2} \leq 2 x$

$x^{2} + 2 x - 35 \geq 0$

$x^{2} + 7 x - 5 x - 35 \geq 0$

$(x + 7) (x - 5) \geq 0$

$x \in [- \infty, - 7] \cup [5, \infty)$

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