Issolvi (sqrt{6}+5)^2-(sqrt{6}+5)

$$( \sqrt { 6 } + 5 ) ^ { 2 } - ( \sqrt { 6 } + 5 )$$

Evalwa

$$9\sqrt{6}+26\approx 48.045407685$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{6}+5\right)^{2}.

$$\left(\sqrt{6}\right)^{2}+10\sqrt{6}+25-\left(\sqrt{6}+5\right)$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$6+10\sqrt{6}+25-\left(\sqrt{6}+5\right)$$

Żid 6 u 25 biex tikseb 31.

$$31+10\sqrt{6}-\left(\sqrt{6}+5\right)$$

Biex issib l-oppost ta' \sqrt{6}+5, sib l-oppost ta' kull terminu.

$$31+10\sqrt{6}-\sqrt{6}-5$$

Ikkombina 10\sqrt{6} u -\sqrt{6} biex tikseb 9\sqrt{6}.

$$31+9\sqrt{6}-5$$

Naqqas 5 minn 31 biex tikseb 26.

$$26+9\sqrt{6}$$

Fattur

$$9 \sqrt{6} + 26 = 48.045407685$$