Giúp Bài Phương Trình Mũ Của Đề Chuyên Lam Sơn

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Câu này hay mà không làm được,ai giúp với...................................................................
 
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conga222222

Câu 9a: Giải phương trình:
$$ (2+\sqrt{3})^{x^2+1} + (2-\sqrt{3})^{x^2-4x-4}=4.(2+\sqrt{3})^{2x+1}$$
Mong mấy thầy cô và các bạn giúp 1 tí ^^!

Câu này hay mà không làm được,ai giúp với...................................................................

\[\begin{array}{*{20}{l}}
{{{\left( {\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)} \right)}^{{x^2} - 4x - 4}} = 1}\\
{pt \leftrightarrow {{\left( {2 + \sqrt 3 } \right)}^{{x^2} + 1}}{{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 4x - 4}} + 1 = 4{{\left( {2 + \sqrt 3 } \right)}^{2x + 1}}{{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 4x - 4}}}\\
{ \leftrightarrow {{\left( {2 + \sqrt 3 } \right)}^{2{x^2} - 4x - 3}} + 1 = {{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 2x - 3}}}\\
{a = {{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 2x - 3}}}\\
{ \to {{\left( {2 + \sqrt 3 } \right)}^3}{a^2} + 1 = a}\\
{ \leftrightarrow ...}
\end{array}\]
 
Last edited by a moderator:
M

magiciancandy

\[\begin{array}{*{20}{l}}
{{{\left( {\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)} \right)}^{{x^2} - 4x - 4}} = 1}\\
{pt \leftrightarrow {{\left( {2 + \sqrt 3 } \right)}^{{x^2} + 1}}{{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 4x - 4}} + 1 = 4{{\left( {2 + \sqrt 3 } \right)}^{2x + 1}}{{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 4x - 4}}}\\
{ \leftrightarrow {{\left( {2 + \sqrt 3 } \right)}^{2{x^2} - 4x - 3}} + 1 = {{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 2x - 3}}}\\
{a = {{\left( {2 + \sqrt 3 } \right)}^{{x^2} - 2x - 3}}}\\
{ \to {{\left( {2 + \sqrt 3 } \right)}^3}{a^2} + 1 = a}\\
{ \leftrightarrow ...}
\end{array}\]


conga222222 ơi, mình tính ra nó vô nghiệm,bạn xem lại có nhầm chỗ nào không,chứ ít khi đề cho vô nghiệm lắm.
 
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conga222222 ơi, mình tính ra nó vô nghiệm,bạn xem lại có nhầm chỗ nào không,chứ ít khi đề cho vô nghiệm lắm.

con này nó cho vô nghiệm vì nếu mà cho có nghiệm thì tính khó lắm bạn để ý là trong cái phương trình bậc hai kia có (2+căn3) nếu mà có nghiệm thì tính delta rồi tính a1 a2 thì còn có thể cố sức làm được nhưng đến lúc thay a vào tính x thì bạn tính đến cả ngày may ra mới xong vì nó có rất nhiều căn tính rất vất vả nên nó cho vô nghiệm để không phải tính
 
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