The equation $$cos8x+bcos4x+1=0$$ will have a solution if b∈$$($$−∞,−k], then $$k+962=$$

We have $$cos8x+bcos4x+1=0$$⇒$$b=-cos4x+1cos4x$$≤$$-2$$ ⇒b≤$$-2$$ ⇒b∈$$($$−∞,−$$2$$] ⇒$$k=2$$ ∴$$k+962=49$$

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The equation $\cos^{8} x + b \cos^{4} x + 1 = 0$ will have a solution if $b \in (- \infty, - k]$ , then $\frac{k + 96}{2} =$

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Solution

We have $\cos^{8} x + b \cos^{4} x + 1 = 0$
$\Rightarrow b = - (\cos^{4} x + \frac{1}{\cos^{4} x}) \leq - 2 \Rightarrow b \leq - 2 \Rightarrow b \in (- \infty, - 2] \Rightarrow k = 2 ∴ \frac{k + 96}{2} = 49$

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