Question

I'll mark u as ✨BRainLieSt✨
plz don't give useless answers

if "10.099" is the answer
give me solution

Answer 1

Hy there,
The answer is
x2=102

⟹x2−102=2

⟹(x−10)(x+10)=2

⟹x=10+210+x

Now substitute this expression for x into the right-hand side of this equation:

⟹x=10+210+10+210+x=10+110+110+x

And we can keep substituting like that ad infinitum:

x=10+110+120+110+120+110+1⋯

As we make more and more substitutions, these fraction towers (called (partial) continued fractions) become arbitrarily close to each other. A good rational approximation is thus

10+110+120+110+120=10+404040601

This gives 10.0995049⋯