Question

помогите срочно !!!!!даю 30 баллов!!!!​

Answer 1

$\left \{ {{a+b=10} \atop {a^2+b^2=8^2}} \right.\; \; \left \{ {{b=10-a\qquad \; \; } \atop {a^2+(10-a)^2=64}} \right.\; \; \left \{ {{b=10-a\qquad \; \; \; } \atop {2a^2-20a+36=0}\; \; }\right.\; \left \{ {{b=10-a\qquad } \atop {a^2-10a+18=0}} \right.\\\\\left \{ {{b_1=5-\sqrt7\; ,\; b_2=5+\sqrt7} \atop {a_1=5+\sqrt7\; ,\; a_2=5-\sqrt7}} \right.\; \; \; \; c^2=a^2+b^2=(5+\sqrt7)^2+(5-\sqrt7)^2=64\; ,\; c=8\\\\P=a+b+c=5+\sqrt7+5-\sqrt7+8=18\\\\p=P:2=18:2=9\\\\S=pr\; \; \to \; \; \; r=\frac{S}{p}$

$S=\sqrt{p(p-a)(p-b)(p-c)}=\sqrt{9(9-5-\sqrt7)(9-5+\sqrt7)(9-8)}=\\\\=\sqrt{9(4-\sqrt7)(4+\sqrt7)}=\sqrt{9(16-7)}=\sqrt{9\cdot 9}=9\\\\r=\frac{S}{p}=\frac{9}{9}=1$