Question

решите 10 и 12плиз очень нужно

Answer 1

Задача 10

$Delta ABC:; 6^2 + x^2 = (5 + y)^2.\CD^2 = 5cdot y.\\Delta CDB:; CD^2 = x^2 - 5^2.$

Решаем систему.

$begin{cases}6^2 + x^2 = (5 + y)^2,\5y = x^2 - 5^2;end{cases}Longleftrightarrow;+begin{cases}36 + x^2 = 25 + y^2 + 10y,\5y - x^2 + 25 = 0.end{cases}\36 + 5y + 25 = 25 + y^2 + 10y;\y^2 + 5y - 36 = 0;\y_{1,2} = dfrac{-5pmsqrt{25 + 4cdot36}}{2} = left[begin{array}{c}4,&-9;end{array}Longrightarrow ;y = 4.$

$5cdot4 - x^2 + 25 = 0;\x^2 = 45;\x_{1,2} = pmsqrt{45};\x_{1,2} = left[begin{array}{c}3sqrt{5},&-3sqrt{5};end{array}Longrightarrow ;x = 3sqrt{5}.$

Ответ: $3sqrt5$.

Задача 12

$AE = dfrac{AD-BC}{2} = dfrac{9-5}{2} = 2.\\BE= sqrt{BA^2-AE^2} = sqrt{6^2-2^2} = sqrt{36-4} = sqrt{32} = 4sqrt2.$

Ответ: $bf4sqrt2$.