Question

5Csqrt%7B%20%5Cleft%7C%20x%20%5Cright%7C%20%7D%20%5Cright%29%20%7D%5E%7B%202%20%7D%20%3D%201" id="TexFormula1" title=" \large \tt \: { x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1" alt=" \large \tt \: { x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1" align="absmiddle" class="latex-formula">
Solve for y. Attach a graph too.
Note :- The graph will come in the shape of a heart.

Only solve if you know it!​​

Answer 1

Refer to the attachment

Answer 2

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

• $\large \tt \: { x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

${ x }^{ 2 } + { \left( y- \sqrt{ \left| x \right| } \right) }^{ 2 } = 1$

Subtract x² from both sides of the equation.

$\left(y-\sqrt{|x|}\right)^{2}+x^{2}-x^{2}=1-x^{2}$

Subtracting x² from itself leaves 0.

$\left(y-\sqrt{|x|}\right)^{2}=1-x^{2}$

Take the square root of both sides of the equation.

$y-\sqrt{|x|}=\sqrt{1-x^{2}} \\ y-\sqrt{|x|}=-\sqrt{1-x^{2}}$

Subtract − √∣x∣ from both sides of the equation.

$y-\sqrt{|x|}-\left(-\sqrt{|x|}\right)=\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) \\ y-\sqrt{|x|}-\left(-\sqrt{|x| } \right)=-\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right)$

Subtracting − √∣x∣ from itself leaves 0.

$y=\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right) \\ y=-\sqrt{1-x^{2}}-\left(-\sqrt{|x|}\right)$

Subtract − √∣x∣from √1- x².

$\underline{\underline{ \sf \: y=\sqrt{1-x^{2}}+\sqrt{|x|} }}$

Subtract − √∣x∣from - √1- x².

$\underline{\underline{ \sf \: y= - \sqrt{1-x^{2}}+\sqrt{|x|} }}$

The equation is now solved.

$\large \boxed{ \boxed{ \bf \: y=\sqrt{1-x^{2}}+\sqrt{|x|} }}\\ \\ \large\boxed {\boxed{ \bf \: y=-\sqrt{1-x^{2}}+\sqrt{|x|} }}$

_________________________________

• Refer to the attached image for the graph.