[tex]9x^4-4=0\\\\9x^4=4\\\\x^4=\frac{4}{9}|\sqrt{}\\\\x^2=\frac{2}{3}\ \vee \ x^2=-\frac{2}{3}\\\\x^2=\frac{2}{3}\\\\x_1=\frac{\sqrt{2}}{\sqrt{3}}\ \vee \ x_2=-\frac{\sqrt{2}}{\sqrt{3}}\\\\x_1=\frac{\sqrt{6}}{3}\ \vee \ x_2=-\frac{\sqrt{6}}{3}\\[/tex]
Równanie ma dwa rozwiązania.
Odpowiedź:
[tex]\huge\boxed {~~Odp.~~C.~2~~}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy ze wzoru skróconego mnożenia
Obliczamy :
[tex]9x^{4} -4=0\\\\(3x^{2} )^{2}-2^{2}=0\\\\(3x^{2} -2)(3x^{2} +2)=0\\\\((\sqrt{3} x)^{2}-(\sqrt{2} )^{2})(3x^{2} +2)=0\\\\(\sqrt{3} x-\sqrt{2})(\sqrt{3} x+\sqrt{2} )(3x^{2} +2)=0\\\\\sqrt{3} x-\sqrt{2} =0~~\lor~~\sqrt{3} x+\sqrt{2} =0~~\lor~~3x^{2} +2=0~~\Rightarrow ~x\in \varnothing \\\\\sqrt{3} x=\sqrt{2} ~~\lor~~\sqrt{3} x=-\sqrt{2} \\\\x=\dfrac{\sqrt{2} }{\sqrt{3} } ~~\lor~~x=-\dfrac{\sqrt{2} }{\sqrt{3} }\\\\\\x=\dfrac{\sqrt{6} }3} ~~\lor ~~x=-\dfrac{\sqrt{6} }{3}[/tex]
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Verified answer
[tex]9x^4-4=0\\\\9x^4=4\\\\x^4=\frac{4}{9}|\sqrt{}\\\\x^2=\frac{2}{3}\ \vee \ x^2=-\frac{2}{3}\\\\x^2=\frac{2}{3}\\\\x_1=\frac{\sqrt{2}}{\sqrt{3}}\ \vee \ x_2=-\frac{\sqrt{2}}{\sqrt{3}}\\\\x_1=\frac{\sqrt{6}}{3}\ \vee \ x_2=-\frac{\sqrt{6}}{3}\\[/tex]
Równanie ma dwa rozwiązania.
Odpowiedź:
[tex]\huge\boxed {~~Odp.~~C.~2~~}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy ze wzoru skróconego mnożenia
Obliczamy :
[tex]9x^{4} -4=0\\\\(3x^{2} )^{2}-2^{2}=0\\\\(3x^{2} -2)(3x^{2} +2)=0\\\\((\sqrt{3} x)^{2}-(\sqrt{2} )^{2})(3x^{2} +2)=0\\\\(\sqrt{3} x-\sqrt{2})(\sqrt{3} x+\sqrt{2} )(3x^{2} +2)=0\\\\\sqrt{3} x-\sqrt{2} =0~~\lor~~\sqrt{3} x+\sqrt{2} =0~~\lor~~3x^{2} +2=0~~\Rightarrow ~x\in \varnothing \\\\\sqrt{3} x=\sqrt{2} ~~\lor~~\sqrt{3} x=-\sqrt{2} \\\\x=\dfrac{\sqrt{2} }{\sqrt{3} } ~~\lor~~x=-\dfrac{\sqrt{2} }{\sqrt{3} }\\\\\\x=\dfrac{\sqrt{6} }3} ~~\lor ~~x=-\dfrac{\sqrt{6} }{3}[/tex]