Tim x
a, (3x-1) ² – 9x(x+2) = 0
b, 25x ² – 9 = 0
c, (4x – 3) (4x+3) – (4x- 5) ² = 46
d, (x+1) ³- (x-1) ³ – 6(x- 1) ² = -10
giúp mình với .
Tim x
a, (3x-1) ² – 9x(x+2) = 0
b, 25x ² – 9 = 0
c, (4x – 3) (4x+3) – (4x- 5) ² = 46
d, (x+1) ³- (x-1) ³ – 6(x- 1) ² = -10
giúp mình với .
Đáp án:
$\begin{array}{l}
a){\left( {3x – 1} \right)^2} – 9x\left( {x + 2} \right) = 0\\
\Rightarrow 9{x^2} – 6x + 1 – 9{x^2} – 18x = 0\\
\Rightarrow – 24x + 1 = 0\\
\Rightarrow 24x = 1\\
\Rightarrow x = \dfrac{1}{{24}}\\
Vay\,x = \dfrac{1}{{24}}\\
b)25{x^2} – 9 = 0\\
\Rightarrow {x^2} = \dfrac{9}{{25}}\\
\Rightarrow \left[ \begin{array}{l}
x = \dfrac{3}{5}\\
x = – \dfrac{3}{5}
\end{array} \right.\\
c)\left( {4x – 3} \right)\left( {4x + 3} \right) – {\left( {4x – 5} \right)^2} = 46\\
\Rightarrow {\left( {4x} \right)^2} – 9 – \left( {16{x^2} – 2.4x.5 + 25} \right) = 46\\
\Rightarrow 16{x^2} – 9 – 16{x^2} + 40x – 25 = 46\\
\Rightarrow 40x = 46 + 9 + 25\\
\Rightarrow 40x = 80\\
\Rightarrow x = 2\\
Vay\,x = 2\\
d){\left( {x + 1} \right)^3} – {\left( {x – 1} \right)^3} – 6{\left( {x – 1} \right)^2} = – 10\\
\Rightarrow {x^3} + 3{x^2} + 3x + 1 – \left( {{x^3} – 3{x^2} + 3x – 1} \right)\\
– 6\left( {{x^2} – 2x + 1} \right) = – 10\\
\Rightarrow 6{x^2} + 2 – 6{x^2} + 12x – 6 = – 10\\
\Rightarrow 12x = – 6\\
\Rightarrow x = – \dfrac{1}{2}\\
Vay\,x = – \dfrac{1}{2}
\end{array}$