1а у²-25х² 2а 9с²-4р∧4
1б у²-25х² 2б 4ф²-16б∧6
1в 25х²-у² 2в х∧6у∧4-1
4х²-19х+32=-6х²-6х+41
Решение:
10х²-13х-9=0
D=169+4*10*9=529
х1,2=13±23/20
х1=36/20=9/5=1ц 4/5=1,8
х2=-10/20=-1/2=-0,5
Ответ: х1=1,8; х2=-0,5
<span>1). Преобразуйте в многочлен:
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![a)~ (a-3)^2=a^2-2\cdot a\cdot3+3^2=a^2-6a+9\\ \\ b)~ (2x+y)^2=(2x)^2+2\cdot2x\cdot y+y^2=4x^2+4xy+y^2\\ \\ c)~ (5b-4x)(5b+4x)=(5b)^2-(4x)^2=25b^2-16x^2](https://tex.z-dn.net/?f=a%29~%20%28a-3%29%5E2%3Da%5E2-2%5Ccdot%20a%5Ccdot3%2B3%5E2%3Da%5E2-6a%2B9%5C%5C%20%5C%5C%20b%29~%20%282x%2By%29%5E2%3D%282x%29%5E2%2B2%5Ccdot2x%5Ccdot%20y%2By%5E2%3D4x%5E2%2B4xy%2By%5E2%5C%5C%20%5C%5C%20c%29~%20%285b-4x%29%285b%2B4x%29%3D%285b%29%5E2-%284x%29%5E2%3D25b%5E2-16x%5E2)
<span>2). Упростите выражение:
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![(a-9)^2-(81+2a)=a^2-18a+81-81-2a=a^2-20a](https://tex.z-dn.net/?f=%28a-9%29%5E2-%2881%2B2a%29%3Da%5E2-18a%2B81-81-2a%3Da%5E2-20a)
<span>3). Разложите на множители:
a) Применим здесь формулу разности квадратов:
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![x^2-25=x^2-5^2=(x-5)(x+5)](https://tex.z-dn.net/?f=x%5E2-25%3Dx%5E2-5%5E2%3D%28x-5%29%28x%2B5%29)
![b)~ ab^2-ac^2=a(b^2-c^2)=a(b-c)(b+c)\\ \\ c)~ -3a^2-6ab-3ab^2=-3a(a+2b+b^2)](https://tex.z-dn.net/?f=b%29~%20ab%5E2-ac%5E2%3Da%28b%5E2-c%5E2%29%3Da%28b-c%29%28b%2Bc%29%5C%5C%20%5C%5C%20c%29~%20-3a%5E2-6ab-3ab%5E2%3D-3a%28a%2B2b%2Bb%5E2%29)
<span>4). Решите уравнение:
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![(2-x)^2-x(x+1.5)=4\\ \\ 4-4x+x^2-x^2-1.5x=4\\ \\ -5.5x=0\\ \\ x=0](https://tex.z-dn.net/?f=%282-x%29%5E2-x%28x%2B1.5%29%3D4%5C%5C%20%5C%5C%204-4x%2Bx%5E2-x%5E2-1.5x%3D4%5C%5C%20%5C%5C%20-5.5x%3D0%5C%5C%20%5C%5C%20x%3D0)
<span>5). Выполните действия:
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![a)~ (y^2-2a)(2a+y^2)=y^4-4a^2\\ \\ b)~ (3x^2+x)^2=9x^4+6x^3+x^2\\ \\ c)~ (2+t)^2(2-t)^2=(4-t^2)^2=16-8t^2+t^4](https://tex.z-dn.net/?f=a%29~%20%28y%5E2-2a%29%282a%2By%5E2%29%3Dy%5E4-4a%5E2%5C%5C%20%5C%5C%20b%29~%20%283x%5E2%2Bx%29%5E2%3D9x%5E4%2B6x%5E3%2Bx%5E2%5C%5C%20%5C%5C%20c%29~%20%282%2Bt%29%5E2%282-t%29%5E2%3D%284-t%5E2%29%5E2%3D16-8t%5E2%2Bt%5E4)
<span>6). Разложите на множители:
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![a)~ 4x^2y^2-9a^4=(2xy)^2-(3a^2)^2=(2xy+3a^2)(2xy-3a^2)\\ \\ b)~ 25a^2-(a+3)^2=(5a-a-3)(5a+a+3)=3(4a-3)(2a+1)\\ \\ c)~27a^3+b^3=(3a+b)(9a^2-3ab+b^2)](https://tex.z-dn.net/?f=a%29~%204x%5E2y%5E2-9a%5E4%3D%282xy%29%5E2-%283a%5E2%29%5E2%3D%282xy%2B3a%5E2%29%282xy-3a%5E2%29%5C%5C%20%5C%5C%20b%29~%2025a%5E2-%28a%2B3%29%5E2%3D%285a-a-3%29%285a%2Ba%2B3%29%3D3%284a-3%29%282a%2B1%29%5C%5C%20%5C%5C%20c%29~27a%5E3%2Bb%5E3%3D%283a%2Bb%29%289a%5E2-3ab%2Bb%5E2%29)
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