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Question Number 222007 by klipto last updated on 14/Jun/25

x(√(1+x^2 ))+log(x+(√(1+x^2 )))=12.5  find x^2  (answer should not be in decimal)

$$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$

Commented by AntonCWX8 last updated on 15/Jun/25

Do you mean to find a close form?

$${Do}\:{you}\:{mean}\:{to}\:{find}\:{a}\:{close}\:{form}? \\ $$

Commented by klipto last updated on 15/Jun/25

yes

$$\boldsymbol{\mathrm{yes}} \\ $$

Commented by AntonCWX8 last updated on 15/Jun/25

Also, do you mean log_(10)  or ln?  Just to make sure

$${Also},\:{do}\:{you}\:{mean}\:{log}_{\mathrm{10}} \:{or}\:{ln}? \\ $$$${Just}\:{to}\:{make}\:{sure} \\ $$

Commented by klipto last updated on 15/Jun/25

log_(10)

$$\boldsymbol{\mathrm{log}}_{\mathrm{10}} \\ $$

Commented by AntonCWX8 last updated on 15/Jun/25

Right.

$${Right}. \\ $$

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