Toán Lớp 9: giải pt :
∛(x ³+5x ²) -1= √ [(5x ²-2)/6 ]
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Toán Lớp 9: giải pt :
∛(x ³+5x ²) -1= √ [(5x ²-2)/6 ]
Comments ( 1 )
$ PT <=> 6(y – 1)^{2} = 5x^{2} – 2 (y >= 1) (**)$
$ <=> 6y^{2} – 12y + 6 = y^{3} – x^{3} – 2$
$ <=> x^{3} = y^{3} – 6y^{2} + 12y – 8$
$ <=> x^{3} = (y – 2)^{3}$
$ <=> x = y – 2 <=> x + 2 = y $
$ <=> (x + 2)^{3} = y^{3}$
$ <=> x^{3} + 6x^{2} + 12x + 8 = x^{3} + 5x^{2}$
$ <=> x^{2} + 12x + 8 = 0$
$ => x = – 6 + 2\sqrt{7} (TM (*);(**))$
(loại $: x = – 6 – 2\sqrt{7} $( ko $TM (**))$