Consider curves $S_1:\sqrt{\left|x\right|}+\sqrt{\left|y\right|}=\sqrt{a},S_2:x^2+y^2=a^2\text{and}{S}_3\text{: }\left|x\right|+\left|y\right|=a.\text{ If }\alpha \text{ is area bounded by }{S}_1\text{and}{S}_2,\beta \text{ is area bounded by }{S}_1\text{and}{S}_3\text{and}\gamma$ is the area bounded by $S_2\text{and}{S}_3,$ then

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