Question

`\large \tt \: { x }^( 2 ) + x \right^( 2 ) = 1`

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

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

• 
  `\large \tt \: { x }^( 2 ) + ) \right) ^( 2 ) = 1`

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

`{ x }^( 2 ) + \left( y- √( \left^( 2 ) = 1`

Subtract x² from both sides of the equation.

`\left(y-√(|x|)\right)^(2)+x^(2)-x^(2)=1-x^(2)`

Subtracting x² from itself leaves 0.

`\left(y-√(|x|)\right)^(2)=1-x^(2)`

Take the square root of both sides of the equation.

`y-√(|x|)=\sqrt{1-x^(2)} \\ y-√(|x|)=-\sqrt{1-x^(2)}`

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

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

Subtracting − √∣x∣ from itself leaves 0.

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

Subtract − √∣x∣from √1- x².

`\underline{\underline{ \sf \: y=\sqrt{1-x^(2)}+√(|x|) }}`

Subtract − √∣x∣from - √1- x².

`\underline{\underline{ \sf \: y= - \sqrt{1-x^(2)}+√(|x|) }}`

The equation is now solved.

`\large \boxed{ \boxed{ \bf \: y=\sqrt{1-x^(2)}+√(|x|) }}\\ \\ \large\boxed {\boxed{ \bf \: y=-\sqrt{1-x^(2)}+√(|x|) }}`

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• Refer to the attached image for the graph.