(8/1*9 + 8/9*17 + 8/17*25+….+ 8/49*57)+58/57+2(x-1)= 2x+7/3 + 5x-8/4
Đề bài : giải phương trình ạ!
mong mn giúp!!!
(8/1*9 + 8/9*17 + 8/17*25+….+ 8/49*57)+58/57+2(x-1)= 2x+7/3 + 5x-8/4
Đề bài : giải phương trình ạ!
mong mn giúp!!!
Đáp án: $x=4$
Giải thích các bước giải:
Ta có:
$\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+…+\dfrac{8}{49.57}$
$=\dfrac{9-1}{1.9}+\dfrac{17-9}{9.17}+\dfrac{25-17}{17.25}+…+\dfrac{57-49}{49.57}$
$=\dfrac11-\dfrac19+\dfrac19-\dfrac1{17}+\dfrac1{17}-\dfrac1{25}+…+\dfrac1{49}-\dfrac1{57}$
$=1-\dfrac1{57}$
$=\dfrac{56}{57}$
Từ đó ta suy ra:
$\dfrac{56}{57}+\dfrac{58}{57}+2(x-1)=\dfrac{2x+7}{3}+\dfrac{5x-8}{4}$
$\to 2+2\left(x-1\right)=\dfrac{2x+7}{3}+\dfrac{5x-8}{4}$
$\to 2\cdot \:12+2\left(x-1\right)\cdot \:12=\dfrac{2x+7}{3}\cdot \:12+\dfrac{5x-8}{4}\cdot \:12$
$\to 24+24\left(x-1\right)=4\left(2x+7\right)+3\left(5x-8\right)$
$\to 24x=23x+4$
$\to x=4$