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1)![(xy) ^{3/4} : \sqrt{x} =x ^{1/4} y ^{3/4} (xy) ^{3/4} : \sqrt{x} =x ^{1/4} y ^{3/4}](https://tex.z-dn.net/?f=%28xy%29+%5E%7B3%2F4%7D+%3A+%5Csqrt%7Bx%7D+%3Dx+%5E%7B1%2F4%7D+y+%5E%7B3%2F4%7D+)
2)![( x^{3/4} y ^{1/4} - x^{1/4} y ^{3/4} )*x/( \sqrt{x} - \sqrt{y)} ( \sqrt{x} + \sqrt{y} )(x+y)= ( x^{3/4} y ^{1/4} - x^{1/4} y ^{3/4} )*x/( \sqrt{x} - \sqrt{y)} ( \sqrt{x} + \sqrt{y} )(x+y)=](https://tex.z-dn.net/?f=%28+x%5E%7B3%2F4%7D+y+%5E%7B1%2F4%7D+-+x%5E%7B1%2F4%7D+y+%5E%7B3%2F4%7D+%29%2Ax%2F%28+%5Csqrt%7Bx%7D+-+%5Csqrt%7By%29%7D+%28+%5Csqrt%7Bx%7D+%2B+%5Csqrt%7By%7D+%29%28x%2By%29%3D)
![(xy) ^{1/4} ( \sqrt{x} - \sqrt{y} )*x/( \sqrt{x} - \sqrt{y} )( \sqrt{x} + \sqrt{y} )(x+y)= (xy) ^{1/4} ( \sqrt{x} - \sqrt{y} )*x/( \sqrt{x} - \sqrt{y} )( \sqrt{x} + \sqrt{y} )(x+y)=](https://tex.z-dn.net/?f=%28xy%29+%5E%7B1%2F4%7D+%28+%5Csqrt%7Bx%7D+-+%5Csqrt%7By%7D+%29%2Ax%2F%28+%5Csqrt%7Bx%7D+-+%5Csqrt%7By%7D+%29%28+%5Csqrt%7Bx%7D+%2B+%5Csqrt%7By%7D+%29%28x%2By%29%3D)
![x*(xy) ^{1/4} /( \sqrt{x} + \sqrt{y} )(x+y) x*(xy) ^{1/4} /( \sqrt{x} + \sqrt{y} )(x+y)](https://tex.z-dn.net/?f=x%2A%28xy%29+%5E%7B1%2F4%7D+%2F%28+%5Csqrt%7Bx%7D+%2B+%5Csqrt%7By%7D+%29%28x%2By%29)
3)![\sqrt[4]{x/y} + \sqrt[4]{y/x} =( \sqrt{x} + \sqrt{y} )/(xy) ^{1/4} \sqrt[4]{x/y} + \sqrt[4]{y/x} =( \sqrt{x} + \sqrt{y} )/(xy) ^{1/4}](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7Bx%2Fy%7D+%2B+%5Csqrt%5B4%5D%7By%2Fx%7D+%3D%28+%5Csqrt%7Bx%7D+%2B+%5Csqrt%7By%7D+%29%2F%28xy%29+%5E%7B1%2F4%7D+)
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