2 câu trả lời
$\sqrt{2\left(x^2+5x+4\right)}+\sqrt{x^2-1}=2x+2$
$⇔\sqrt{2x^2+10x+8}+\sqrt{x^2-1}=2x+2$
$⇔\sqrt{2\left(x+1\right)\left(x+4\right)}+\sqrt{\left(x+1\right)\left(x-1\right)}=2x+2$
$⇔2x^2+10x+8+\left(2x+2\right)\cdot \:2\left(x+4\right)\left(x-1\right)+\left(x+1\right)\left(x-1\right)=4x^2+8x+4$
$⇔4x^3+19x^2+6x-9=4x^2+8x+4$
$⇔4x^3+15x^2-2x-13=0$
\(⇔\left[ \begin{array}{l}x+1=0\\\:4x^2+11x-13=0\end{array} \right.\) \(⇔\left[ \begin{array}{l}x=-1(tm)\\x=\dfrac{-11+\sqrt{329}}{8},\:x=\dfrac{-11-\sqrt{329}}{8}(ktm)\end{array} \right.\)
$\text{Vậy pt có nghiệm S = {-1}}$
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