If $\lim _{x\to 0}\frac{{e}^{ax}-\cos (bx)-\frac{cx{e}^{-cx}}{2}}{1-\cos (2x)}=17$, then $5{a}^{2}+{b}^{2}$ is equal to [JEE Main 2023, 13 Apr (Shift 2)]

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If \(\lim _{x\to 0}\frac{{e}^{ax}-\cos (bx)-\frac{cx{e}^{-cx}}{2}}{1-\cos (2x)}=17\), then \(5{a}^{2}+{b}^{2}\) is equal…

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