(x -1)^2 = (11-x)^ 2
x - 1 = 11 - x или x - 1 = x - 11
2x = 12
x = 6
Ответ: 6
<span><span><span>−3</span>,<span><span><span>5<span>x2</span></span>+<span>6x</span></span>−0</span></span>,<span>5=0</span></span>
<span>Коэффициенты уравнения: </span>
<span><span>a=<span>−3</span></span>,5</span><span>, </span><span>b=6</span><span>, </span><span><span>c=<span>−0</span></span>,5</span>
<span>Вычислим дискриминант: </span>
<span><span>D=<span><span>b2</span>−<span><span>4a</span>c</span></span></span>=</span><span><span><span><span>62</span>−<span><span>4·<span>(<span><span>−3</span>,5</span>)</span></span>·<span>(<span><span>−0</span>,5</span>)</span></span></span>=<span>36−7</span></span>=29</span>
<span>(<span>D>0</span>)</span>, следовательно это квадратное уравнение имеет 2 различных вещественных корня:
Вычислим корни:
<span><span>x<span>(<span>1,2</span>)</span></span>=<span><span><span>−b</span>±<span>√D</span></span><span>2a
</span></span></span><span><span><span><span><span><span>x1</span>=<span><span><span>−b</span>+<span>√D</span></span><span>2a</span></span></span>=<span><span><span><span>−6</span>+5</span>,385</span><span>2·<span>(<span><span>−3</span>,5</span>)</span></span></span></span>=<span><span><span>−0</span>,615</span><span>−7</span></span></span>=0</span>,088
</span><span><span><span><span><span><span>x2</span>=<span><span><span>−b</span>−<span>√D</span></span><span>2a</span></span></span>=<span><span><span><span>−6</span>−5</span>,385</span><span>2·<span>(<span><span>−3</span>,5</span>)</span></span></span></span>=<span><span><span>−11</span>,385</span><span>−7</span></span></span>=1</span>,626</span>
<span><span><span>−3</span>,<span><span><span>5<span>x2</span></span>+<span>6x</span></span>−0</span></span>,<span><span>5=<span>0.5·<span><span>(<span><span>x−0</span>,088</span>)</span><span>(<span><span>x−1</span>,626</span>)</span></span></span></span>=0
</span></span>Ответ:
<span><span><span>x1</span>=0</span>,088</span>
<span><span><span>x2</span>=1</span>,<span>626</span></span>
(3n+4)²=9n²+24n+16
2) (x-5y)²=x²-10xy+25y²
3) (2\3a-b)(2\3a+b)=(2\3a)²-b²=4\9a²-b²
3sin^2(x)+2sinx*cosx-2sin^2(x)-2cos^2(x)=0
sin^2(x)+2sinx*cosx-2cos^2(x)=0 получили однородное уравнение поделим на сos^2(x)
tg^2(x)+2tg(x)-2=0 tg(x)=y
y^2+2y-2=0
D=4+4*2=12 тут не знаю мож ошибся где
y1,2=-2+-2/2
tgx=-2+-2/2
x=arctg(-2+-2/2)+pi<var>k</var>