Draw the graph of sqrt(|x|) + sqrt(|y|)=...

Draw the graph of `sqrt(|x|) + sqrt(|y|)=1`

Text Solution

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`|sqrt(x)|+|sqrt(y)|=1`
Let `x,y gt 0`
`therefore sqrt(x) + sqrt(y)=`
`therefore sqrt(y)=1-sqrt(x)`
Clearly `1-sqrt(x) gt 0` or `0 lt x lt 1`
Similarly `0 to y to 1`
For `x=0, y=1`
For `y=0, x=1`
Also, `y=(1-sqrt(x))^(2) lt 1 - sqrt(x) lt 1 -x`
That is, the graph of `sqrt(y)=1-sqrt(x)` lies below the graph of `x+y=1` as shown in the following figure.
Similarly, we have branches in each quadrant.

Finally, we have the following graph for all cases as shown in the following figure.

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