2х +2(х+2)+4+16=х (х+2) решаете квадратное уравнение и получаете х=3 - ширина домика, х+2=5- длина домика
При a≥8; оригинале задаче пропущено.
![\sqrt{(\sqrt{a+4\sqrt{a-4}}-\sqrt{a-4\sqrt{a-4}})^2}=](https://tex.z-dn.net/?f=%5Csqrt%7B%28%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D%7D-%5Csqrt%7Ba-4%5Csqrt%7Ba-4%7D%7D%29%5E2%7D%3D)
![\sqrt{a+4\sqrt{a-4}-2\sqrt{a+4\sqrt{a-4}}\sqrt{a-4\sqrt{a-4}} +a-4\sqrt{a-4}}=](https://tex.z-dn.net/?f=%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D-2%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D%7D%5Csqrt%7Ba-4%5Csqrt%7Ba-4%7D%7D%20%2Ba-4%5Csqrt%7Ba-4%7D%7D%3D)
![\sqrt{2a-2\sqrt{a^2-16(a-4)}}=\sqrt{2a-2\sqrt{a^2-16a+64}}=\sqrt{2a-2\sqrt{(a-8)^2}}=\sqrt{2a-2(a-8)}}=\sqrt{2a-2a+16}}=\sqrt{16}=4](https://tex.z-dn.net/?f=%5Csqrt%7B2a-2%5Csqrt%7Ba%5E2-16%28a-4%29%7D%7D%3D%5Csqrt%7B2a-2%5Csqrt%7Ba%5E2-16a%2B64%7D%7D%3D%5Csqrt%7B2a-2%5Csqrt%7B%28a-8%29%5E2%7D%7D%3D%5Csqrt%7B2a-2%28a-8%29%7D%7D%3D%5Csqrt%7B2a-2a%2B16%7D%7D%3D%5Csqrt%7B16%7D%3D4)
㏒ₐ(а³/b⁵) = ㏒ₐa³-㏒ₐb⁵=3*㏒ₐa-5*㏒ₐb=3*1-5-7=3-35= -32
1/2*lg81 - lg x > lg2
lg√81 - lgx > lg2
lg9 - lgx > lg2
lgx < lg9 - lg2
lgx < lg(9:2)
lgx < lg4,5
x < 4,5
x∈(-∞; 4,5)