Issolvi -5sqrt{2}-(sqrt{5}-sqrt{2})^2

$$- 5 \sqrt { 2 } - ( \sqrt { 5 } - \sqrt { 2 } ) ^ { 2 }$$

Evalwa

$$2\sqrt{10}-5\sqrt{2}-7\approx -7.746512492$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\sqrt{5}-\sqrt{2}\right)^{2}.

$$-5\sqrt{2}-\left(\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$-5\sqrt{2}-\left(5-2\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Biex timmultiplika \sqrt{5} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$-5\sqrt{2}-\left(5-2\sqrt{10}+\left(\sqrt{2}\right)^{2}\right)$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$-5\sqrt{2}-\left(5-2\sqrt{10}+2\right)$$

Żid 5 u 2 biex tikseb 7.

$$-5\sqrt{2}-\left(7-2\sqrt{10}\right)$$

Biex issib l-oppost ta' 7-2\sqrt{10}, sib l-oppost ta' kull terminu.

$$-5\sqrt{2}-7+2\sqrt{10}$$