Odpowiedź:
Pełna odpowiedź poniżej
Szczegółowe wyjaśnienie:
[tex]x + y = 7 \\ x \times y = \frac{45}{4} \\ x = 7 - y \\ (7 - y) \times y = \frac{45}{4} \\ 7y - {y}^{2} - \frac{45}{4} = 0 \\ - {y}^{2} + 7y - \frac{45}{4} = 0 \\ delta = 49 - 4 \times ( - 1) \times ( - \frac{45}{4} ) \\ delta = 49 - 45 = 4 \\ \sqrt{delta} = 2 \\ y1 = \frac{ - 7 - 2}{ - 2} = 4.5 \\ y2 = \frac{ - 7 + 2}{ - 2} = 2.5 \\ x1 = 2.5 \\ x2 = 4.5 \\ {x}^{2} + {y}^{2} = {4.5}^{2} + {2.5}^{2} = 26.5 = \frac{53}{2} [/tex]
[tex]\begin{aligned}\\&a+b=7\\&ab=\dfrac{45}{4}\\&a^2+b^2=?\end{aligned}\\\\\\(a+b)^2=a^2+2ab+b^2\\a^2+b^2=(a+b)^2-2ab\\\\a^2+b^2=7^2-2\cdot\dfrac{45}{4}=49-\dfrac{45}{2}=\dfrac{98}{2}-\dfrac{45}{2}=\dfrac{53}{2}[/tex]
