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Oznaczmy różnicę jako a: a=17−122<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M1001 80h400000v40h-400000z'/></svg>​ &nbsp; Podnieśmy obie strony równości do potegi drugiej: a2=(17−122<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M1001 80h400000v40h-400000z'/></svg>​−17+122<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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a) 327+64+125<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​=6

a) (32<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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M834 80h400000v40h-400000z'/></svg>​+25<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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M834 80h400000v40h-400000z'/></svg>​)(32<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​−25<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​)2−(25<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​)2=18−20=−2 &nbsp;

a) 23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​37<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​⋅3<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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a) a<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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H400000v40H845.2724
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M834 80h400000v40h-400000z'/></svg>​−b<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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H400000v40H845.2724
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M834 80h400000v40h-400000z'/></svg>​x​ Założenia: a≥0   i   b≥0   i   a<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​−b<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​=0 Warunek &nbsp;√a-√b=0 jest spełniony, gdy a=b. Stąd warunek √a-√b≠0 jest spełniony dla a≠b. Ostatecznie otrzymujemy założenie: a≥0,  b≥0,  a=b &nbsp; Usuwamy niewymierność z mianownika:

Oznaczmy różnicę jako a: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1cad6078b8fa6d26bb7b826a476dbf6cb1304abfb20d02a6fa124d51de6b57b5_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1cad6078b8fa6d26bb7b826a476dbf6cb1304abfb20d02a6fa124d51de6b57b5_big.svg" type="image/svg+xml"></object> &nbsp; Podnieśmy obie strony równości do potegi drugiej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e9fd82818e27f3a5b583e35f1b86c0f265a5584e927aa76d1fe35943cf89f7f7_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e9fd82818e27f3a5b583e35f1b86c0f265a5584e927aa76d1fe35943cf89f7f7_big.svg" type="image/svg+xml"></object>

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