Issolvi (1+5sqrt{2})(1-2sqrt{2})-sqrt{18}

$$(1+5 \sqrt{ 2 } )(1-2 \sqrt{ 2 } )- \sqrt{ 18 }$$

Evalwa

$$-19$$

Passi tas-Soluzzjonijiet

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 1+5\sqrt{2} b'kull terminu ta' 1-2\sqrt{2}.

$$1-2\sqrt{2}+5\sqrt{2}-10\left(\sqrt{2}\right)^{2}-\sqrt{18}$$

Ikkombina -2\sqrt{2} u 5\sqrt{2} biex tikseb 3\sqrt{2}.

$$1+3\sqrt{2}-10\left(\sqrt{2}\right)^{2}-\sqrt{18}$$

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

$$1+3\sqrt{2}-10\times 2-\sqrt{18}$$

Immultiplika -10 u 2 biex tikseb -20.

$$1+3\sqrt{2}-20-\sqrt{18}$$

Naqqas 20 minn 1 biex tikseb -19.

$$-19+3\sqrt{2}-\sqrt{18}$$

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$-19+3\sqrt{2}-3\sqrt{2}$$

Ikkombina 3\sqrt{2} u -3\sqrt{2} biex tikseb 0.

$$-19$$

Fattur

$$-19$$