Question

-) Розв'яжіть рівняння 16-9y² = 0. -​

Answer 1

Первый способ :

$\displaystyle\bf\\16-9y^{2}=0\\\\4^{2} -(3y)^{2} =0\\\\(4-3y)\cdot(4+3y)=0\\\\\\\left[\begin{array}{ccc}4-3y=0\\4+3y=0\end{array}\right\\\\\\\left[\begin{array}{ccc}3y=4\\3y=-4\end{array}\right\\\\\\\left[\begin{array}{ccc}y_{1} =1\dfrac{1}{3} \\y_{2} =-1\frac{1}{3} \end{array}\right$

Второй способ :

$\displaystyle\bf\\16-9y^{2} =0\\\\9y^{2} =16\\\\y^{2}=\frac{16}{9} \\\\\\y_{1,2} =\pm \ \sqrt{\frac{16}{9} } =\pm \ \sqrt{\Big(\frac{4}{3} \Big)^{2} } =\pm \ \frac{4}{3} =\pm \ 1\frac{1}{3}\\\\\\Otvet : \ -1\frac{1}{3} \ \ ; \ \ 1\frac{1}{3}$