Toán Lớp 8: x ² – 7x – 4 √x + 20=0 (x ≥ 0)
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Toán Lớp 8: x ² – 7x – 4 √x + 20=0 (x ≥ 0)
Comments ( 1 )
{a^4} – 7{a^2} – 4a + 20 = 0\\
\Leftrightarrow {a^4} – 2{a^3} + 2{a^3} – 4{a^2} – 3{a^2} + 6a – 10a + 20 = 0\\
\Leftrightarrow {a^3}\left( {a – 2} \right) + 2{a^2}\left( {a – 2} \right) – 3a\left( {a – 2} \right) – 10\left( {a – 2} \right) = 0\\
\Leftrightarrow \left( {a – 2} \right)\left( {{a^3} + 2{a^2} – 3a – 10} \right) = 0\\
\Leftrightarrow \left( {a – 2} \right)\left[ {{a^3} – 2{a^2} + 4{a^2} – 8a + 5a – 10} \right] = 0\\
\Leftrightarrow {\left( {a – 2} \right)^2}\underbrace {\left( {{a^2} + 4a + 5} \right)}_{ > 0} = 0\\
\Leftrightarrow a = 2 \Leftrightarrow \sqrt x = 2 \Leftrightarrow x = 4
\end{array}$