Example

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

Question

$$\sqrt{ 3 { x }^{ 2 } +4 } =2 \sqrt{ 2 { \left( { x }^{ 2 } \right) }^{ 24 } }$$

Answer

x=-0.99717178344727,0.99717178344727

Solution


Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\sqrt{3{x}^{2}+4}=2\sqrt{2{x}^{48}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\sqrt{3{x}^{2}+4}=2\sqrt{{x}^{48}}\sqrt{2}\]
Simplify  \(\sqrt{{x}^{48}}\)  to  \({x}^{24}\).
\[\sqrt{3{x}^{2}+4}=2{x}^{24}\sqrt{2}\]
Simplify square root.
\[\sqrt{3{x}^{2}+4}=2\sqrt{2}{x}^{24}\]
Square both sides.
\[3{x}^{2}+4=8{x}^{48}\]
Move all terms to one side.
\[3{x}^{2}+4-8{x}^{48}=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=\pm 0.997172\]
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