Buktikan bahwa (a^2-b^2),2ab,(a^2+b^2) membentuk tripel pythagoras

tripel phytagoras a^2 + b^2 = c^2

[tex]dalam \: phytagoras \: berlaku \\ {a}^{2} + {b}^{2} = {c}^{2} \\ \\ dalam \: soal \\ a = {a}^{2} - {b}^{2} \\ b = 2ab \\ c = {a}^{2} + {b}^{2} \\ \\ maka \\ ( {a}^{2} - {b}^{2} ) ^{2} + (2 {ab})^{2} = ( {a}^{2} + {b}^{2} )^{2} \\ {a}^{4} - 2 {a}^{2} {b}^{2} + {b}^{4} + 4 {a}^{2} {b}^{2} = ( {a}^{2} + {b}^{2} )^{2} \\ {a}^{4} + 2 {a}^{2} {b}^{2} + {b}^{4} = ( {a}^{2} + {b}^{2} )^{2} \\ ( {a}^{2} + {b}^{2} )^{2} = ( {a}^{2} + {b}^{2} )^{2} \\ \\ terbukti[/tex]
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