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Question Number 149060 by mathdanisur last updated on 02/Aug/21

if 4z(√z) − 11(√z) = 5 find 2z − (√z) = ?

$${if}\:\:\:\mathrm{4}{z}\sqrt{{z}}\:−\:\mathrm{11}\sqrt{{z}}\:=\:\mathrm{5} \\ $$$${find}\:\:\:\mathrm{2}{z}\:−\:\sqrt{{z}}\:=\:? \\ $$

Answered by bramlexs22 last updated on 02/Aug/21

⇒(√z) = u ⇒4z(√z)−(√z) = 5+10(√z) ⇒(√z) (4z−1)=5(1+2(√z) ) ⇒(√z) (2(√z)−1)(2(√z)+1)=5(2(√z)+1) ⇒(2(√z)+1){(√z) (2(√z)−1)−5}=0 2(√z) +1 = 0 ⇇ not possible (√z) (2(√z)−1)−5=0 ⇒2z−(√z) = (√z) (2(√z)−1)= 5

$$\Rightarrow\sqrt{\mathrm{z}}\:=\:\mathrm{u}\: \\ $$$$\Rightarrow\mathrm{4z}\sqrt{\mathrm{z}}−\sqrt{\mathrm{z}}\:=\:\mathrm{5}+\mathrm{10}\sqrt{\mathrm{z}} \\ $$$$\Rightarrow\sqrt{\mathrm{z}}\:\left(\mathrm{4z}−\mathrm{1}\right)=\mathrm{5}\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{z}}\:\right) \\ $$$$\Rightarrow\sqrt{\mathrm{z}}\:\left(\mathrm{2}\sqrt{\mathrm{z}}−\mathrm{1}\right)\left(\mathrm{2}\sqrt{\mathrm{z}}+\mathrm{1}\right)=\mathrm{5}\left(\mathrm{2}\sqrt{\mathrm{z}}+\mathrm{1}\right) \\ $$$$\Rightarrow\left(\mathrm{2}\sqrt{\mathrm{z}}+\mathrm{1}\right)\left\{\sqrt{\mathrm{z}}\:\left(\mathrm{2}\sqrt{\mathrm{z}}−\mathrm{1}\right)−\mathrm{5}\right\}=\mathrm{0} \\ $$$$\mathrm{2}\sqrt{\mathrm{z}}\:+\mathrm{1}\:=\:\mathrm{0}\:\leftleftarrows\:\mathrm{not}\:\mathrm{possible} \\ $$$$\sqrt{\mathrm{z}}\:\left(\mathrm{2}\sqrt{\mathrm{z}}−\mathrm{1}\right)−\mathrm{5}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{2z}−\sqrt{\mathrm{z}}\:=\:\sqrt{\mathrm{z}}\:\left(\mathrm{2}\sqrt{\mathrm{z}}−\mathrm{1}\right)=\:\mathrm{5} \\ $$$$ \\ $$

Commented by mathdanisur last updated on 02/Aug/21

Thank You Ser

$${Thank}\:{You}\:{Ser} \\ $$

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