Ответ:
4a+49b
Пошаговое объяснение:
![\displaystyle\\\\ \frac{8a^{\frac{3}{2}}-343b^{\frac{3}{2}}}{2a^{\frac{1}{2}}+7b^{\frac{1}{2}}}*\frac{4a-49b}{4a+14a^{\frac{1}{2}}b^{\frac{1}{2}}+49b} +28a^{\frac{1}{2}}b^{\frac{1}{2}}=\\\\\displaystyle\\\frac{(2a^\frac{1}{2})^3-(7b^\frac{1}{2})^3}{2a^{\frac{1}{2}}+7b^{\frac{1}{2}}} *\frac{(2a^{\frac{1}{2}}+7b^{\frac{1}{2}})(2a^{\frac{1}{2}}-7b^{\frac{1}{2}})}{(2a^{\frac{1}{2}})^2+2a^{\frac{1}{2}} *7b^{\frac{1}{2}}+(7b^{\frac{1}{2}})^2} +28a^{\frac{1}{2}}b^{\frac{1}{2}}=\\\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%5C%5C%20%5Cfrac%7B8a%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D-343b%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%7B2a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%2A%5Cfrac%7B4a-49b%7D%7B4a%2B14a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B49b%7D%20%2B28a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5C%5C%5C%5C%5Cdisplaystyle%5C%5C%5Cfrac%7B%282a%5E%5Cfrac%7B1%7D%7B2%7D%29%5E3-%287b%5E%5Cfrac%7B1%7D%7B2%7D%29%5E3%7D%7B2a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%20%2A%5Cfrac%7B%282a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%282a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D-7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%7D%7B%282a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5E2%2B2a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%2A7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B%287b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5E2%7D%20%2B28a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5C%5C%5C%5C)
![\displaystyle\\(2a^\frac{1}{2}-7b^{\frac{1}{2}})^2+28a^{\frac{1}{2}}b^{\frac{1}{2}}=4a-28a^{\frac{1}{2}}b^{\frac{1}{2}}+49b+28a^{\frac{1}{2}}b^{\frac{1}{2}}=4a+49b\\ \\ \\](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%282a%5E%5Cfrac%7B1%7D%7B2%7D-7b%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5E2%2B28a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D4a-28a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2B49b%2B28a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Db%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D4a%2B49b%5C%5C%20%5C%5C%20%5C%5C)
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использованы формулы:
a³-b³=(a-b)(a²+ab+b²) разность кубов
a²-b²=(a-b)(a+b) разность квадратов
(a-b)²=a²-2ab+b² квадрат разности
1)7,4*0,8=5,92
2)172*0,01=1,72
3)11,84/5,92=2
4)2+1,72=3,72
65-40= 25 - ( книг на 2 ой полки) , 65+25=90 - (книг на 3 ей полки .