[tex]a - cateta \: 1 \\ b - cateta \: 2 \\ c - ipotenuza[/tex]
[tex]a = b - 4[/tex]
[tex] {a}^{2} + {b}^{2} = {c}^{2} \:(teorema\: lui\:Pitagora)[/tex]
[tex] {(b - 4)}^{2} + {b}^{2} = {20}^{2} [/tex]
[tex] {b}^{2} - 8b + 16 + {b}^{2} = 400[/tex]
[tex] {b}^{2} + {b}^{2} - 8b + 16 - 400 = 0[/tex]
[tex]2 {b}^{2} - 8b - 384 = 0 \: | \div 2[/tex]
[tex] {b}^{2} - 4b - 192 = 0[/tex]
[tex]x = 1[/tex]
[tex]y = - 4[/tex]
[tex]z = - 192[/tex]
[tex]\Delta = {y}^{2} - 4xz[/tex]
[tex]\Delta = {( - 4)}^{2} - 4 \times 1 \times ( - 192)[/tex]
[tex]\Delta = 16 + 768[/tex]
[tex]\Delta = 784[/tex]
[tex]b_{1,2}=\frac{-y\pm\sqrt{\Delta}}{2x}
[/tex]
[tex]b_{1,2}=\frac{-( - 4)\pm\sqrt{784}}{2 \times 1}
[/tex]
[tex]b_{1,2}=\frac{4\pm28}{2 }[/tex]
[tex]b_{1}=\frac{4 + 28}{2 }[/tex]
[tex]b_{1}=\frac{32}{2 }[/tex]
[tex]b_{1}=16[/tex]
[tex]b_{2}=\frac{4 - 28}{2 }[/tex]
[tex]b_{2}= - \frac{24}{2 }[/tex]
[tex]b_{2}= - 12 \: nu \: convine[/tex]
[tex] = > b = 16 \: cm[/tex]
[tex]a = b - 4[/tex]
[tex]a = 16 - 4[/tex]
[tex]a = 12[/tex]
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {12}^{2} + {16}^{2} = {20}^{2} [/tex]
[tex]144 + 256 = 400[/tex]
[tex]400 = 400 \: (A)[/tex]
