Toán Lớp 9: 2x − 3 = \sqrt{ 3 x − 4} − \sqrt{x − 1}
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Toán Lớp 9: 2x − 3 = \sqrt{ 3 x − 4} − \sqrt{x − 1}
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– TH1 $ : a – b = 0 <=> a = b <=> x = \dfrac{3}{2} (TM)$
– TH2 $ : a + b – 1 = 0 <=> a + b = 1$
$ <=> a^{2} + b^{2} + 2ab = 1$
$ <=> ab = 3 – 2x $
$ <=> a^{2}b^{2} = (3 – 2x)^{2} ( \dfrac{4}{3} =< x =< \dfrac{3}{2})$
$ <=> 3x^{2} – 7x + 4 = 9 – 12x + 4x^{2}$
$ <=> x^{2} – 5x + 5 = 0 $
$ <=> x = \dfrac{5 – \sqrt{5}}{2} (TM)$ (loại $ x = \dfrac{5 + \sqrt{5}}{2})$