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Sa sa e rezolve in multimea numerelor reale ecuatia √15-3x=1+x

Răspuns :

[tex] \sqrt{15} -3x=1+x \\ \sqrt{15} = 1 +x+3x \\ \sqrt{15} = 1+4x \\ 15 = 1+8x+16x^{2} \\ 16 x^{2} +8x-14 = 0|:2 \\ 8 x^{2} +4x - 7 = 0[/tex]

Δ=16+4*8*7 = 16+224=240
[tex] x_{1,2} = \frac{-4 +- \sqrt{240} }{16} = \frac{-4+-4 \sqrt{15} }{16} = \frac{-1+- \sqrt{15} }{4} [/tex]