Question

Resolva detalhada a equação de segundo grau: 8-x/2-x+6/2=2x-11/x-3 (sendo x diferente 3)

Answer 1

$\frac{8-x}{2}-\frac{x+6}{2}=\frac{2x-11}{x-3}\\\\mmc(2,x-3)=2.(x-3)\\\\(x-3).(8-x)-(x-3).(x+6)=2.(2x-11)\\\\8x-x^{2}-24+3x-(x^{2}+6x-3x-18)=4x-22\\\\8x-x^{2}-24+3x-x^{2}-6x+3x+18-4x+22=0\\\\-2x^{2}+4x+16=0:(2)\\\\-x^{2}+2x+8=0\\\\a=-1,b=2,c=8$

Δ = $b^{2}-4ac$

Δ = $(2)^{2}-4.(-1).(8)$

Δ = $4+32$

Δ = $36$

$x=\frac{-b\±\sqrt{\delta}}{2a}\\\\x=\frac{-(2)\±\sqrt{36}}{2(-1)}\\\\x=\frac{-2\±6}{-2}\\\\x'=\frac{-2+6}{-2}=\frac{4}{-2}=-2\\\\x'=\frac{-2-6}{-2}=\frac{-8}{-2}=4$

$S=\{-2,4\}$