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tia_tia [17]
1 year ago
5

Pls help me solve this question, also include step by step calculation ya. Thks

Mathematics
1 answer:
sp2606 [1]1 year ago
6 0

\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}

Step-by-step explanation:

5x^2-x^2e^{2x}+2e^{2x}=10

Let:\ x^2=t  \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}

<em>Prologarithmize both parts of the equation:</em>

ln5=lne^{2x}\\ln5=2x*lne\\ln5=2x*1\\ln5=2x\\

<u><em> Divide both parts of the equation by 2:</em></u>

\displaystyle\\x=\frac{ln5}{2}

t-2=0\\t-2+2=0+2\\t=2\\x^2=2\\x=\sqrt{2} \\x=-\sqrt{2}

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