[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- [tex] \large \tt \: { x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]{ x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1[/tex]
Subtract x² from both sides of the equation.
[tex]\left(y-\sqrt{|x|}\right)^{2}+x^{2}-x^{2}=1-x^{2} [/tex]
Subtracting x² from itself leaves 0.
[tex]\left(y-\sqrt{|x|}\right)^{2}=1-x^{2} [/tex]
Take the square root of both sides of the equation.
[tex]y-\sqrt{|x|}=\sqrt{1-x^{2}} \\ y-\sqrt{|x|}=-\sqrt{1-x^{2}} [/tex]
Subtract − √∣x∣ from both sides of the equation.
[tex]y-\sqrt{|x|}-\left(-\sqrt{|x|}\right)=\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) \\ y-\sqrt{|x|}-\left(-\sqrt{|x| } \right)=-\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) [/tex]
Subtracting − √∣x∣ from itself leaves 0.
[tex]y=\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) \\ y=-\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) [/tex]
Subtract − √∣x∣from √1- x².
[tex] \underline{\underline{ \sf \: y=\sqrt{1-x^{2}}+\sqrt{|x|} }}[/tex]
Subtract − √∣x∣from - √1- x².
[tex] \underline{\underline{ \sf \: y= - \sqrt{1-x^{2}}+\sqrt{|x|} }}[/tex]
The equation is now solved.
[tex] \large \boxed{ \boxed{ \bf \: y=\sqrt{1-x^{2}}+\sqrt{|x|} }}\\ \\ \large\boxed {\boxed{ \bf \: y=-\sqrt{1-x^{2}}+\sqrt{|x|} }}[/tex]
_________________________________
- Refer to the attached image for the graph.
