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Question Number 54582 by Tawa1 last updated on 07/Feb/19

Solve for x:     (1/(√(x + (√x) + 1))) + (2/(√(x + (√x) − 2)))  = (√(x + 1))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\frac{\mathrm{1}}{\sqrt{\mathrm{x}\:+\:\sqrt{\mathrm{x}}\:+\:\mathrm{1}}}\:+\:\frac{\mathrm{2}}{\sqrt{\mathrm{x}\:+\:\sqrt{\mathrm{x}}\:−\:\mathrm{2}}}\:\:=\:\sqrt{\mathrm{x}\:+\:\mathrm{1}} \\ $$

Commented by MJS last updated on 07/Feb/19

with t=(√x) and squaring etc. this leads to a  polynome of degree 12  we can only approximate.  ⇒ x≈2.4474286375747

$$\mathrm{with}\:{t}=\sqrt{{x}}\:\mathrm{and}\:\mathrm{squaring}\:\mathrm{etc}.\:\mathrm{this}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{a} \\ $$$$\mathrm{polynome}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{12} \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate}. \\ $$$$\Rightarrow\:{x}\approx\mathrm{2}.\mathrm{4474286375747} \\ $$

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