If the domain of the function \(f\left(x\right)=\frac{1}{\sqrt{10+3\mathrm{x}-{\mathrm{x}}^{2}}}+\frac{1}{\sqrt{\mathrm{…

If the domain of the function \(f\left(x\right)=\frac{1}{\sqrt{10+3\mathrm{x}-{\mathrm{x}}^{2}}}+\frac{1}{\sqrt{\mathrm{x}+|\mathrm{x}|}}\) is \((a,b)\), then \((1+\mathrm{a}{)}^{2}+{\mathrm{b}}^{2}\)is equal to :

[JEE Main 2025, 2 Apr (Shift 2)]