Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$ProveThat \sqrt{ 2 } isirrational$$

Answer

$$-Pr*eTh*sqrt(2)*IM*o^2*v*a^3*t^2*s*r^2*n*l$$

Solution


Regroup terms.
\[oovaaattsrrnlPreTh\sqrt{2}\imath \imath \imath \]
Simplify.
\[{o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nlPreTh\sqrt{2}\imath \imath \imath \]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nlPreTh\sqrt{2}{\imath }^{3}\]
Isolate \({\imath }^{2}\).
\[{o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nlPreTh\sqrt{2}{\imath }^{2}\imath \]
Use Square Rule: \({i}^{2}=-1\).
\[{o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nlPreTh\sqrt{2}\times -1\times \imath \]
Simplify.
\[{o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nlPreTh\sqrt{2}\times -\imath \]
Regroup terms.
\[-PreTh\sqrt{2}\imath {o}^{2}v{a}^{3}{t}^{2}s{r}^{2}nl\]
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