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Question Number 140503 by ERA last updated on 08/May/21
Prove it  (√(a+(√b)))=(√(((a+(√(a^2 +b)))/2)+))(√((a−(√(a^2 −b)))/2))
$$\boldsymbol{\mathrm{P}}\mathrm{rove}\:\mathrm{it} \\ $$$$\sqrt{\boldsymbol{{a}}+\sqrt{\boldsymbol{{b}}}}=\sqrt{\frac{\boldsymbol{{a}}+\sqrt{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}}}{\mathrm{2}}+}\sqrt{\frac{\boldsymbol{{a}}−\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{b}}}}{\mathrm{2}}} \\ $$
Commented by MJS_new last updated on 08/May/21
it′s wrong
$$\mathrm{it}'\mathrm{s}\:\mathrm{wrong} \\ $$
Commented by MJS_new last updated on 10/May/21
it′s still wrong
$$\mathrm{it}'\mathrm{s}\:\mathrm{still}\:\mathrm{wrong} \\ $$
Commented by Dwaipayan Shikari last updated on 10/May/21
It should be (√((a+(√(a^2 −b)))/2))+(√((a−(√(a^2 −b)))/2))
$${It}\:{should}\:{be}\:\sqrt{\frac{{a}+\sqrt{{a}^{\mathrm{2}} −{b}}}{\mathrm{2}}}+\sqrt{\frac{{a}−\sqrt{{a}^{\mathrm{2}} −{b}}}{\mathrm{2}}} \\ $$

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