Question

\(\dfrac{x-11}{89}+\dfrac{x-13}{87}+\dfrac{x-15}{85}+\dfrac{x-17}{83}=4\)

Answer 1

\(\dfrac{x-11}{89}\) +\(\dfrac{x-13}{87}+\dfrac{x-15}{85}+\dfrac{x-17}{83}\)=4

⇔\(\dfrac{x-11}{89}+\dfrac{x-13}{87}+\dfrac{x-15}{85}+\dfrac{x-17}{83}-4=0\)

⇔\(\dfrac{x-11}{89}-1+\dfrac{x-13}{87}-1+\dfrac{x-15}{85}-1+\dfrac{x-17}{83}-1=0\)

⇔\(\dfrac{x-100}{89}+\dfrac{x-100}{87}+\dfrac{x-100}{85}+\dfrac{x-100}{83}=0\)

⇔\(\left(x-100\right)\left(\dfrac{1}{89}+\dfrac{1}{87}+\dfrac{1}{85}+\dfrac{1}{83}\right)=0\)

\(Do\) \(\dfrac{1}{89}+\dfrac{1}{87}+\dfrac{1}{85}+\dfrac{1}{83}\)≠\(0\) nên x-100=0 nên x=100

KL........

Answer 2

⇔(\(\dfrac{x-11}{89}\)-1)+(\(\dfrac{x-13}{87}\)-1)+(\(\dfrac{x-15}{85}\)-1)+(\(\dfrac{x-17}{83}\)-1)=0

⇔\(\dfrac{x-100}{89}\)+\(\dfrac{x-100}{87}\)+\(\dfrac{x-100}{85}\)+\(\dfrac{x-100}{83}\)=0

⇔(x-100)(\(\dfrac{1}{89}\)+\(\dfrac{1}{87}\)+\(\dfrac{1}{85}\)+\(\dfrac{1}{83}\))=0 (1)

Do 1/89+1/87+1/85+1/83≠0 nên (1)⇔x-100=0 ⇔x=100

Vậy tập nghiệm của PT là S=\(\left\{100\right\}\)