Question

a) Giải phương trình: (x - 187)/13 + (x - 170)/15 + (x - 149)/17 + (x - 124)/19 = 10

Answer 1

\(\dfrac{x-187}{13}+\dfrac{x-170}{15}+\dfrac{x-149}{17}+\dfrac{x-124}{19}=10\)

`<=>(x-187)/13+(x-170)/15+(x-149)/17+(x-124)/19-10=0`

`<=>(x-187)/13-1+(x-170)/15-2+(x-149)/17-3+(x-124)/19-4=0`

`<=>(x-200)/13+(x-200)/15+(x-200)/17+(x-200)/19=0`

`<=>(x-200)(1/13+1/15+1/17+1/19)=0`

`<=>x-200=0(1/13+1/15+1/17+1/19>0)`

`<=>x=200`

Answer 2

\(=>\left(\dfrac{x-187}{13}-1\right)+\left(\dfrac{x-170}{15}-2\right)+\left(\dfrac{x-149}{17}-3\right)+\left(\dfrac{x-124}{19}-4\right)=0\)\(< =>\left(\dfrac{x-187}{13}-\dfrac{13}{13}\right)+\left(\dfrac{x-170}{15}-\dfrac{30}{15}\right)+\left(\dfrac{x-149}{17}-\dfrac{51}{17}\right)+\left(\dfrac{x-124}{19}-\dfrac{76}{19}\right)=0\)

\(< =>\left(\dfrac{x-200}{13}\right)+\left(\dfrac{x-200}{15}\right)+\left(\dfrac{x-200}{17}\right)+\left(\dfrac{x-200}{19}\right)=0\)

\(< =>\left(x-200\right)\left(\dfrac{1}{13}+\dfrac{1}{15}+\dfrac{1}{17}+\dfrac{1}{19}\right)=0\)

\(< =>x-200=0\)

<=>x=200

Answer 3

=>\(\left(\dfrac{x-187}{13}-1\right)+\left(\dfrac{x-170}{15}-2\right)+\left(\dfrac{x-149}{17}-3\right)+\left(\dfrac{x-124}{19}-4\right)=0\)

=>x-200=0

=>x=200