Question

rezolvati ecuatia de gradul 2 (x-1)(x-3)(x-5)(x-7)=-15 printr.o notatie convenabila...plzz..ajutor...am nevoie urgent!

Answer 1

(x-1)(x-3)(x-5)(x-7)=-15
[(x-1)(x-7)][(x-3)(x-5)]=-15
$(x^{2} -8x+7)( x^{2} -8x+15)=-15 \\ notam \\ x^{2} -8x=t \\ (t+7)(t+15)=-15 \\ t^{2}+22t+120=0$
Δ=4
$t_{1}= \frac{-22-2}{2}=-12; t_{2}= \frac{-22+2}{2}=-10$
revenim la substitutie
$x^{2} -8x=-12; x^{2} -8x=-10\\ x^{2} -8x+12=0; x^{2} -8x+10=0 \\ x=2;x=6;x=[tex]4- \sqrt{6}$;x=[$4+ \sqrt{6}$/tex]
S={2;6;4-√6;4+√6}