Example

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

Question

$$PROVETHAT \sqrt{ 3+ \sqrt{ 2ISan } irrationa \ln ( umber ) }$$

Answer

$$PROVETHATsqrt(3-r^2*a^2*t*o*n*sqrt(2*ISa*n)*ln(u*m*b*e*r))$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[PROVETHATsqrt(3+sqrt(2ISan){\imath }^{2}{r}^{2}{a}^{2}tonln(umber))\]
Use Square Rule: \({i}^{2}=-1\).
\[PROVETHATsqrt(3+sqrt(2ISan)\times -1\times {r}^{2}{a}^{2}tonln(umber))\]
Simplify  \(\sqrt{2ISan}\times -1\times {r}^{2}{a}^{2}ton\ln{(umber)}\)  to  \(\sqrt{2ISan}\times -{r}^{2}{a}^{2}ton\ln{(umber)}\).
\[PROVETHATsqrt(3+sqrt(2ISan)\times -{r}^{2}{a}^{2}tonln(umber))\]
Regroup terms.
\[PROVETHATsqrt(3-{r}^{2}{a}^{2}tonsqrt(2ISan)ln(umber))\]
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