х+7=9 Подставляем "2", получаем: 2+7=9, 9=9 тождество верно. Следовательно 2 явл корнем уравнения.
5х=12 Подставляем "2", получаем: 10=12 тождество неверно. 2 не является корнем уравнения.
<span>х-8=-6 Подставляем "2", получаем: 2-8=-6 тождество верно. Следовательно 2 явл корнем уравнения.
<span>х:4=2 Подставляем "2", получаем: 2:4=0,5( или 1/2) тождество неверно. Следовательно 2 не является корнем уравнения.</span></span>
16x+6x-x^2=0
22x - x^2 = 0
x(22-x) = 0
x=0 и 22-x=0
-x=-22
x=22
<span>Дана система ур-ний</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Из 1-го ур-ния выразим x</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span>Перенесем слагаемое с переменной y из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span>Разделим обе части ур-ния на множитель при x</span>
<span /><span><span><span><span><span><span><span><span><span><span>3</span><span>x</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>1</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>(</span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span>)</span></span></span><span /></span></span><span /></span><span>3x3=13(−y+2)</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>Подставим найденное x в 2-е ур-ние</span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Получим:</span>
<span /><span><span><span><span><span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span><span><span>(</span></span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>)</span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−y+2(−y3+23)=3</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>4</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−5y3+43=3</span></span>
<span>Перенесем свободное слагаемое 4/3 из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span>Разделим обе части ур-ния на множитель при y</span>
<span /><span><span><span><span><span><span><span><span><span><span>−</span><span>1</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>y<span /></span></span><span /></span><span><span><span>−</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span><span><span /><span /></span></span></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>−153y−53=−1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>y=−1</span></span>
<span>Т.к.</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>то</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span><span>−</span><span>1</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−−13+23</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span>Ответ:</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span></span><span>
</span>
a)
0,5x^2-2=0
0,5x^2=2
x^2=2/0,5
x^2=4
x=+-2
б)
-1/3x^2-2x=0
x(-1/3x-2)=0
x1=0
-1/3x-2=0
-1/3=2
x=2:(-1/3)
x2=-6
а графическим методом надо рисовать
Решение: <span>Пятого, у которого скорость 10 км/ч. Будем считать обгоны в тот момент, когда первый догоняет второго велосипедиста. В момент, когда первый проехал 5 икругов, второй проехал 4 круга (его скорость составляет 4/5 от скорости первого), третий – 3 круга, четвертый – 2 круга, пятый 1 круг. В этот момент все велосипедисты опять находятся в одной точке. Тогда к этому моменту первый обогнал второго 1 раз, третьего 2 раза, четвертого – 3 раза, пятого – 4 раза, т.е. первый насчитал 10 велосипедистов, которых он обогнал. После того как первый проедет еще 5 кругов, он насчитает 10 обгонов. В этот момент все велосипедисты опять находятся в одной точке. Тогда первый обгонит и посчитает 21-м самого медленного из велосипедистов — пятого.</span>
