Issolvi sqrt{8}+sqrt{18}+sqrt{1/8}=a+bsqrt{2}

$$\sqrt { 8 } + \sqrt { 18 } + \sqrt { \frac { 1 } { 8 } } = a + b \sqrt { 2 }$$

Solvi għal a

$$a=\frac{\sqrt{2}\left(21-4b\right)}{4}$$

Passi tas-Soluzzjonijiet

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\sqrt{2}+\sqrt{18}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

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}.

$$2\sqrt{2}+3\sqrt{2}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

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

$$5\sqrt{2}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{8}}.

$$5\sqrt{2}+\frac{\sqrt{1}}{\sqrt{8}}=a+b\sqrt{2}$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$5\sqrt{2}+\frac{1}{\sqrt{8}}=a+b\sqrt{2}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$5\sqrt{2}+\frac{1}{2\sqrt{2}}=a+b\sqrt{2}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$5\sqrt{2}+\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}=a+b\sqrt{2}$$

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

$$5\sqrt{2}+\frac{\sqrt{2}}{2\times 2}=a+b\sqrt{2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$5\sqrt{2}+\frac{\sqrt{2}}{4}=a+b\sqrt{2}$$

Ikkombina 5\sqrt{2} u \frac{\sqrt{2}}{4} biex tikseb \frac{21}{4}\sqrt{2}.

$$\frac{21}{4}\sqrt{2}=a+b\sqrt{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$a+b\sqrt{2}=\frac{21}{4}\sqrt{2}$$

Naqqas b\sqrt{2} miż-żewġ naħat.

$$a=\frac{21}{4}\sqrt{2}-b\sqrt{2}$$

Erġa' ordna t-termini.

$$a=-\sqrt{2}b+\frac{21}{4}\sqrt{2}$$

Solvi għal b

$$b=-\frac{\sqrt{2}a}{2}+\frac{21}{4}$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\sqrt{2}+\sqrt{18}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

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}.

$$2\sqrt{2}+3\sqrt{2}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

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

$$5\sqrt{2}+\sqrt{\frac{1}{8}}=a+b\sqrt{2}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{8}}.

$$5\sqrt{2}+\frac{\sqrt{1}}{\sqrt{8}}=a+b\sqrt{2}$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$5\sqrt{2}+\frac{1}{\sqrt{8}}=a+b\sqrt{2}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$5\sqrt{2}+\frac{1}{2\sqrt{2}}=a+b\sqrt{2}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$5\sqrt{2}+\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}=a+b\sqrt{2}$$

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

$$5\sqrt{2}+\frac{\sqrt{2}}{2\times 2}=a+b\sqrt{2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$5\sqrt{2}+\frac{\sqrt{2}}{4}=a+b\sqrt{2}$$

Ikkombina 5\sqrt{2} u \frac{\sqrt{2}}{4} biex tikseb \frac{21}{4}\sqrt{2}.

$$\frac{21}{4}\sqrt{2}=a+b\sqrt{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$a+b\sqrt{2}=\frac{21}{4}\sqrt{2}$$

Naqqas a miż-żewġ naħat.

$$b\sqrt{2}=\frac{21}{4}\sqrt{2}-a$$

L-ekwazzjoni hija f'forma standard.

$$\sqrt{2}b=-a+\frac{21\sqrt{2}}{4}$$

Iddividi ż-żewġ naħat b'\sqrt{2}.

$$\frac{\sqrt{2}b}{\sqrt{2}}=\frac{-a+\frac{21\sqrt{2}}{4}}{\sqrt{2}}$$

Meta tiddividi b'\sqrt{2} titneħħa l-multiplikazzjoni b'\sqrt{2}.

$$b=\frac{-a+\frac{21\sqrt{2}}{4}}{\sqrt{2}}$$

Iddividi \frac{21\sqrt{2}}{4}-a b'\sqrt{2}.

$$b=-\frac{\sqrt{2}a}{2}+\frac{21}{4}$$