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2-x-2-x-2-solve-for-x-




Question Number 170781 by solomonwells last updated on 30/May/22
(√((2−x)))   =  (2−x)^2   solve for      x
$$\sqrt{\left(\mathrm{2}−\mathrm{x}\right)}\:\:\:=\:\:\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} \:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\:\:\:\:\:\boldsymbol{\mathrm{x}} \\ $$
Answered by Rasheed.Sindhi last updated on 30/May/22
(((2−x)^2 )/((2−x)^(1/2) ))=1  (2−x)^(3/2) =1^(3/2)   2−x=1  x=1
$$\frac{\left(\mathrm{2}−{x}\right)^{\mathrm{2}} }{\left(\mathrm{2}−{x}\right)^{\mathrm{1}/\mathrm{2}} }=\mathrm{1} \\ $$$$\left(\mathrm{2}−{x}\right)^{\mathrm{3}/\mathrm{2}} =\mathrm{1}^{\mathrm{3}/\mathrm{2}} \\ $$$$\mathrm{2}−{x}=\mathrm{1} \\ $$$${x}=\mathrm{1} \\ $$
Commented by mr W last updated on 30/May/22
x=2 is also good
$${x}=\mathrm{2}\:{is}\:{also}\:{good} \\ $$
Commented by Rasheed.Sindhi last updated on 30/May/22
Of course sir:  (√(2−x)) =(2−x)^2   (√(2−x)) −(2−x)^2 =0  (√(2−x)) (1−(2−x)^(3/2) )=0  (√(2−x)) =0 ∣ (2−x)^(3/2) =1  x=2      ∣   (2−x)^(3/2) =1^(3/2)                        2−x=1                       x=1
$$\mathrm{Of}\:\mathrm{course}\:\mathrm{sir}: \\ $$$$\sqrt{\mathrm{2}−{x}}\:=\left(\mathrm{2}−{x}\right)^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{2}−{x}}\:−\left(\mathrm{2}−{x}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\sqrt{\mathrm{2}−{x}}\:\left(\mathrm{1}−\left(\mathrm{2}−{x}\right)^{\mathrm{3}/\mathrm{2}} \right)=\mathrm{0} \\ $$$$\sqrt{\mathrm{2}−{x}}\:=\mathrm{0}\:\mid\:\left(\mathrm{2}−{x}\right)^{\mathrm{3}/\mathrm{2}} =\mathrm{1} \\ $$$${x}=\mathrm{2}\:\:\:\:\:\:\mid\:\:\:\left(\mathrm{2}−{x}\right)^{\mathrm{3}/\mathrm{2}} =\mathrm{1}^{\mathrm{3}/\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}−{x}=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\mathrm{1} \\ $$
Answered by MJS_new last updated on 31/May/22
t=(√(2−x)) ≥0 ⇔ x=2−t^2   t=t^4   t(t^3 −1)=0  t=0∨t=1 ⇒ x=1∨x=2
$${t}=\sqrt{\mathrm{2}−{x}}\:\geqslant\mathrm{0}\:\Leftrightarrow\:{x}=\mathrm{2}−{t}^{\mathrm{2}} \\ $$$${t}={t}^{\mathrm{4}} \\ $$$${t}\left({t}^{\mathrm{3}} −\mathrm{1}\right)=\mathrm{0} \\ $$$${t}=\mathrm{0}\vee{t}=\mathrm{1}\:\Rightarrow\:{x}=\mathrm{1}\vee{x}=\mathrm{2} \\ $$

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