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Question Number 128589 by mnjuly1970 last updated on 08/Jan/21

             ...nice  calculus...       a∈R^+                &                  }⇒ (√(a−(√a) )) =?       a^2 −17a=16(√a)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:...{nice}\:\:{calculus}... \\ $$ $$\:\:\:\:\:{a}\in\mathbb{R}^{+} \:\: \\ $$ $$\left.\:\:\:\:\:\:\:\:\:\:\:\&\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right\}\Rightarrow\:\sqrt{{a}−\sqrt{{a}}\:}\:=? \\ $$ $$\:\:\:\:\:{a}^{\mathrm{2}} −\mathrm{17}{a}=\mathrm{16}\sqrt{{a}}\: \\ $$ $$\:\:\:\:\:\:\: \\ $$

Answered by snipers237 last updated on 08/Jan/21

(a−(√a))(a+(√a))=16(a+(√a))⇒(√(a−(√a)))  ∈{0,4}

$$\left({a}−\sqrt{{a}}\right)\left({a}+\sqrt{{a}}\right)=\mathrm{16}\left({a}+\sqrt{{a}}\right)\Rightarrow\sqrt{{a}−\sqrt{{a}}}\:\:\in\left\{\mathrm{0},\mathrm{4}\right\} \\ $$

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