Vyriešiť left(88-90.875right)^2+left(94-90.875right)^2+left(93-90.875right)^2+left(90-90.875right)^2+{left(91-90.875right)}^2+{left(94-90.875right)}^2+{left(90-90.875right)}^2+{left(87-90.875right)}^2

$${ \left(88-90.875 \right) }^{ 2 } + { \left(94-90.875 \right) }^{ 2 } + { \left(93-90.875 \right) }^{ 2 } + { \left(90-90.875 \right) }^{ 2 } + { \left(91-90.875 \right) }^{ 2 } + { \left(94-90.875 \right) }^{ 2 } + { \left(90-90.875 \right) }^{ 2 } + { \left(87-90.875 \right) }^{ 2 }$$

Vyhodnotiť

$$48.875$$

Postup riešenia

Odčítajte 90.875 z 88 a dostanete -2.875.

$$\left(-2.875\right)^{2}+\left(94-90.875\right)^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla -2.875 a dostanete 8.265625.

$$8.265625+\left(94-90.875\right)^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 94 a dostanete 3.125.

$$8.265625+3.125^{2}+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla 3.125 a dostanete 9.765625.

$$8.265625+9.765625+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Sčítaním 8.265625 a 9.765625 získate 18.03125.

$$18.03125+\left(93-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 93 a dostanete 2.125.

$$18.03125+2.125^{2}+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla 2.125 a dostanete 4.515625.

$$18.03125+4.515625+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Sčítaním 18.03125 a 4.515625 získate 22.546875.

$$22.546875+\left(90-90.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 90 a dostanete -0.875.

$$22.546875+\left(-0.875\right)^{2}+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla -0.875 a dostanete 0.765625.

$$22.546875+0.765625+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Sčítaním 22.546875 a 0.765625 získate 23.3125.

$$23.3125+\left(91-90.875\right)^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 91 a dostanete 0.125.

$$23.3125+0.125^{2}+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla 0.125 a dostanete 0.015625.

$$23.3125+0.015625+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Sčítaním 23.3125 a 0.015625 získate 23.328125.

$$23.328125+\left(94-90.875\right)^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 94 a dostanete 3.125.

$$23.328125+3.125^{2}+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla 3.125 a dostanete 9.765625.

$$23.328125+9.765625+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Sčítaním 23.328125 a 9.765625 získate 33.09375.

$$33.09375+\left(90-90.875\right)^{2}+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 90 a dostanete -0.875.

$$33.09375+\left(-0.875\right)^{2}+\left(87-90.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla -0.875 a dostanete 0.765625.

$$33.09375+0.765625+\left(87-90.875\right)^{2}$$

Sčítaním 33.09375 a 0.765625 získate 33.859375.

$$33.859375+\left(87-90.875\right)^{2}$$

Odčítajte 90.875 z 87 a dostanete -3.875.

$$33.859375+\left(-3.875\right)^{2}$$

Vypočítajte 2 ako mocninu čísla -3.875 a dostanete 15.015625.

$$33.859375+15.015625$$

Sčítaním 33.859375 a 15.015625 získate 48.875.

$$48.875$$

Rozložiť na faktory

$$\frac{17 \cdot 23}{2 ^ {3}} = 48\frac{7}{8} = 48.875$$