Дано уравнение: <span><span>4<span>x4</span>−<span>x2</span>=0</span><span>4<span>x4</span>−<span>x2</span>=0</span></span> преобразуем Вынесем общий множитель x^2 за скобки получим: <span><span><span>x2</span><span>(4<span>x2</span>−1)</span>=0</span><span><span>x2</span><span>(4<span>x2</span>−1)</span>=0</span></span> тогда: <span><span><span>x1</span>=0</span><span><span>x1</span>=0</span></span> и также получаем ур-ние <span><span>4<span>x2</span>−1=0</span><span>4<span>x2</span>−1=0</span></span> Это уравнение вида a*x^2 + b*x + c. Квадратное уравнение можно решить с помощью дискриминанта. Корни квадратного уравнения: <span><span><span>x2</span>=<span><span><span>D<span>−−</span>√</span>−b</span><span>2a</span></span></span><span><span>x2</span>=<span><span>D−b</span><span>2a</span></span></span></span> <span><span><span>x3</span>=<span><span>−<span>D<span>−−</span>√</span>−b</span><span>2a</span></span></span><span><span>x3</span>=<span><span>−D−b</span><span>2a</span></span></span></span> где D = b^2 - 4*a*c - это дискриминант. Т.к. <span><span>a=4</span><span>a=4</span></span> <span><span>b=0</span><span>b=0</span></span> <span><span>c=−1</span><span>c=−1</span></span> , то D = b^2 - 4 * a * c = (0)^2 - 4 * (4) * (-1) = 16 Т.к. D > 0, то уравнение имеет два корня. x2 = (-b + sqrt(D)) / (2*a) x3 = (-b - sqrt(D)) / (2*a) или <span><span><span>x2</span>=<span>12</span></span><span><span>x2</span>=<span>12</span></span></span> <span><span><span>x3</span>=−<span>12</span></span><span><span>x3</span>=−<span>12</span></span></span> Получаем окончательный ответ для 4*x^4 - x^2 = 0: <span><span><span>x1</span>=0</span><span><span>x1</span>=0</span></span> <span><span><span>x2</span>=<span>12</span></span><span><span>x2</span>=<span>12</span></span></span> <span><span><span>x3</span>=−<span>12</span></span></span>