Ответы
Ответ дал:
1
a- первый катет
b- второй катет
![\left \{ {{a+b=23} \atop {a^2+b^2=17^2}} \right. \left \{ {{a=23-b} \atop {(23-b)^2+b^2=289}} \right. \\ \left \{ {{a=23-b} \atop {529-46b+b^2+b^2=289}} \right. \left \{ {{a_1=12~b_1=11} \atop {a_2=8~b_2=15}} \right. \\ \\ 2b^2-46b+529-289=0~|:2 \\ b^2-23b+120=0 \\ D=529-480=49 \\ b_1= \frac{23-7}{2} =11 \\ b_2=15 \left \{ {{a+b=23} \atop {a^2+b^2=17^2}} \right. \left \{ {{a=23-b} \atop {(23-b)^2+b^2=289}} \right. \\ \left \{ {{a=23-b} \atop {529-46b+b^2+b^2=289}} \right. \left \{ {{a_1=12~b_1=11} \atop {a_2=8~b_2=15}} \right. \\ \\ 2b^2-46b+529-289=0~|:2 \\ b^2-23b+120=0 \\ D=529-480=49 \\ b_1= \frac{23-7}{2} =11 \\ b_2=15](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Ba%2Bb%3D23%7D+%5Catop+%7Ba%5E2%2Bb%5E2%3D17%5E2%7D%7D+%5Cright.++++%5Cleft+%5C%7B+%7B%7Ba%3D23-b%7D+%5Catop+%7B%2823-b%29%5E2%2Bb%5E2%3D289%7D%7D+%5Cright.++%5C%5C+%5Cleft+%5C%7B+%7B%7Ba%3D23-b%7D+%5Catop+%7B529-46b%2Bb%5E2%2Bb%5E2%3D289%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Ba_1%3D12%7Eb_1%3D11%7D+%5Catop+%7Ba_2%3D8%7Eb_2%3D15%7D%7D+%5Cright.++++%5C%5C++%5C%5C+2b%5E2-46b%2B529-289%3D0%7E%7C%3A2+%5C%5C+b%5E2-23b%2B120%3D0+%5C%5C+D%3D529-480%3D49+%5C%5C+b_1%3D+%5Cfrac%7B23-7%7D%7B2%7D+%3D11+%5C%5C+b_2%3D15)
![\\ Otvet:8~i~15 \\ 17^2=8^2+15^2 \\ 289=289; \\ \\ 17^2=12^2+11^2 \\ 289 \neq 265 \\ Otvet:8~i~15 \\ 17^2=8^2+15^2 \\ 289=289; \\ \\ 17^2=12^2+11^2 \\ 289 \neq 265](https://tex.z-dn.net/?f=+%5C%5C+Otvet%3A8%7Ei%7E15+%5C%5C+17%5E2%3D8%5E2%2B15%5E2+%5C%5C+289%3D289%3B+%5C%5C++%5C%5C+17%5E2%3D12%5E2%2B11%5E2+%5C%5C+289+%5Cneq+265)
b- второй катет
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