Пусть меньшая сторона равна х см. Тогда большая сторона (х+6)см. Составим и решим уравнение:
х(х+6)+65=(х+1)(х+6+2)
х²+6х+65=х²+9х+8
х²-х²+6х-9х=8-65
-3х=-57
3х=57
х=19 (см)
19+6=25см
Ответ: 19см; 25см.
Ай=-31, А=-27 последующее число на 4 больше предыдущего. А31=а1+30*4=-31+120=89
числа 41 нет
1. Выполнить действия :
![\rm a)~4a+\dfrac{1-4a^2}{a}=\dfrac{4a^2+1-4a^2}{a}=\dfrac{1}{a}\\ \\b)~\dfrac{a+b}{a-b}-\dfrac{a-b}{a+b}=\dfrac{(a+b)^2-(a-b)^2}{(a-b)(a+b)}=\dfrac{(a+b+a-b)(a+b-a+b)}{a^2-b^2}=\\ \\=\dfrac{2a\cdot 2b}{a^2-b^2}=\dfrac{4ab}{a^2-b^2}\\ \\ c)~\dfrac{2a-4}{3b}\cdot\dfrac{6b}{a-2}=\dfrac{2(a-2)}{3b}\cdot\dfrac{6b}{a-2}=4\\ \\ d)~\dfrac{a^2-b^2}{b^2}:\dfrac{a+b}{b}=\dfrac{(a-b)(a+b)}{b^2}\cdot\dfrac{b}{a+b}=\dfrac{a-b}{b}](https://tex.z-dn.net/?f=%5Crm+a%29~4a%2B%5Cdfrac%7B1-4a%5E2%7D%7Ba%7D%3D%5Cdfrac%7B4a%5E2%2B1-4a%5E2%7D%7Ba%7D%3D%5Cdfrac%7B1%7D%7Ba%7D%5C%5C+%5C%5Cb%29~%5Cdfrac%7Ba%2Bb%7D%7Ba-b%7D-%5Cdfrac%7Ba-b%7D%7Ba%2Bb%7D%3D%5Cdfrac%7B%28a%2Bb%29%5E2-%28a-b%29%5E2%7D%7B%28a-b%29%28a%2Bb%29%7D%3D%5Cdfrac%7B%28a%2Bb%2Ba-b%29%28a%2Bb-a%2Bb%29%7D%7Ba%5E2-b%5E2%7D%3D%5C%5C+%5C%5C%3D%5Cdfrac%7B2a%5Ccdot+2b%7D%7Ba%5E2-b%5E2%7D%3D%5Cdfrac%7B4ab%7D%7Ba%5E2-b%5E2%7D%5C%5C+%5C%5C+c%29~%5Cdfrac%7B2a-4%7D%7B3b%7D%5Ccdot%5Cdfrac%7B6b%7D%7Ba-2%7D%3D%5Cdfrac%7B2%28a-2%29%7D%7B3b%7D%5Ccdot%5Cdfrac%7B6b%7D%7Ba-2%7D%3D4%5C%5C+%5C%5C+d%29~%5Cdfrac%7Ba%5E2-b%5E2%7D%7Bb%5E2%7D%3A%5Cdfrac%7Ba%2Bb%7D%7Bb%7D%3D%5Cdfrac%7B%28a-b%29%28a%2Bb%29%7D%7Bb%5E2%7D%5Ccdot%5Cdfrac%7Bb%7D%7Ba%2Bb%7D%3D%5Cdfrac%7Ba-b%7D%7Bb%7D)
2. Упростить выражение
![\dfrac{1+2x}{x-3}-\dfrac{x^2+3x}{5}\cdot\dfrac{10}{x^2-9}=\dfrac{1+2x}{x-3}-\dfrac{x(x+3)}{5}\cdot\dfrac{10}{(x-3)(x+3)}=\\ \\ =\dfrac{1+2x}{x-3}-\dfrac{2x}{x-3}=\dfrac{1+2x-2x}{x-3}=\dfrac{1}{x-3}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%2B2x%7D%7Bx-3%7D-%5Cdfrac%7Bx%5E2%2B3x%7D%7B5%7D%5Ccdot%5Cdfrac%7B10%7D%7Bx%5E2-9%7D%3D%5Cdfrac%7B1%2B2x%7D%7Bx-3%7D-%5Cdfrac%7Bx%28x%2B3%29%7D%7B5%7D%5Ccdot%5Cdfrac%7B10%7D%7B%28x-3%29%28x%2B3%29%7D%3D%5C%5C+%5C%5C+%3D%5Cdfrac%7B1%2B2x%7D%7Bx-3%7D-%5Cdfrac%7B2x%7D%7Bx-3%7D%3D%5Cdfrac%7B1%2B2x-2x%7D%7Bx-3%7D%3D%5Cdfrac%7B1%7D%7Bx-3%7D)
Найдем его числовое значение при x = 2 2/3
![\dfrac{1}{x-3}=\dfrac{1}{2\frac{2}{3}-3}=\dfrac{1}{2\frac{2}{3}-2\frac{3}{3}}=\dfrac{1}{-\frac{1}{3}}=-3](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bx-3%7D%3D%5Cdfrac%7B1%7D%7B2%5Cfrac%7B2%7D%7B3%7D-3%7D%3D%5Cdfrac%7B1%7D%7B2%5Cfrac%7B2%7D%7B3%7D-2%5Cfrac%7B3%7D%7B3%7D%7D%3D%5Cdfrac%7B1%7D%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D-3)