Question

Вычислите: (4 1/6)^2 + (1 1/6)^2​

Answer 1

$\left(4\frac16\right)^2+\left(1\frac16\right)^2=\left(\frac{25}6\right)^2+\left(\frac76\right)^2=\frac{625}{36}+\frac{49}{36}=\frac{674}{36}=18\frac{26}{36}=18\frac{13}{18}$

2 вариант:

$x^2+y^2=x^2-2xy+y^2+2xy=(x-y)^2-2xy\\\\\left(4\frac16\right)^2+\left(1\frac16\right)^2=\left(4\frac16-1\frac16\right)^2+2\cdot4\frac16\cdot1\frac16=\\=3^2+2\cdot\frac{25}6\cdot\frac76=9+\frac{25}3\cdot\frac76=9+\frac{175}{18}=9+9\frac{13}{18}=18\frac{13}{18}$