حل 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

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

تقدير القيمة

$$48.875$$

خطوات الحل

اطرح 90.875 من 88 لتحصل على -2.875.

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

احسب -2.875 بالأس 2 لتحصل على 8.265625.

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

اطرح 90.875 من 94 لتحصل على 3.125.

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

احسب 3.125 بالأس 2 لتحصل على 9.765625.

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

اجمع 8.265625 مع 9.765625 لتحصل على 18.03125.

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

اطرح 90.875 من 93 لتحصل على 2.125.

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

احسب 2.125 بالأس 2 لتحصل على 4.515625.

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

اجمع 18.03125 مع 4.515625 لتحصل على 22.546875.

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

اطرح 90.875 من 90 لتحصل على -0.875.

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

احسب -0.875 بالأس 2 لتحصل على 0.765625.

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

اجمع 22.546875 مع 0.765625 لتحصل على 23.3125.

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

اطرح 90.875 من 91 لتحصل على 0.125.

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

احسب 0.125 بالأس 2 لتحصل على 0.015625.

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

اجمع 23.3125 مع 0.015625 لتحصل على 23.328125.

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

اطرح 90.875 من 94 لتحصل على 3.125.

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

احسب 3.125 بالأس 2 لتحصل على 9.765625.

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

اجمع 23.328125 مع 9.765625 لتحصل على 33.09375.

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

اطرح 90.875 من 90 لتحصل على -0.875.

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

احسب -0.875 بالأس 2 لتحصل على 0.765625.

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

اجمع 33.09375 مع 0.765625 لتحصل على 33.859375.

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

اطرح 90.875 من 87 لتحصل على -3.875.

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

احسب -3.875 بالأس 2 لتحصل على 15.015625.

$$33.859375+15.015625$$

اجمع 33.859375 مع 15.015625 لتحصل على 48.875.

$$48.875$$

تحليل العوامل

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