Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$Y^{\wedge}2+X^{\wedge}2=(Y+X)-(Y-X)$$

Answer

Y=sqrt(X*(2-X)),-sqrt(X*(2-X))

Solution


Remove parentheses.
\[{Y}^{2}+{X}^{2}=Y+X-Y+X\]
Simplify  \(Y+X-Y+X\)  to  \(2X\).
\[{Y}^{2}+{X}^{2}=2X\]
Subtract \({X}^{2}\) from both sides.
\[{Y}^{2}=2X-{X}^{2}\]
Take the square root of both sides.
\[Y=\pm \sqrt{2X-{X}^{2}}\]
Factor out the common term \(X\).
\[Y=\pm \sqrt{X(2-X)}\]
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