Bài 1:
\(a,8.6+288.\left(x+3\right)^2=50\\ \Leftrightarrow48+288\left(x+3\right)^2=50\\ \Leftrightarrow\left(x+3\right)^2=\dfrac{1}{144}\\ \Leftrightarrow x+3\in\left\{-\dfrac{1}{12};\dfrac{1}{12}\right\}\\ \Leftrightarrow x\in\left\{-\dfrac{37}{12};-\dfrac{35}{12}\right\}\\ Vậy.....\)
\(b,\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
=>Số lượng số hạng của tổng trên là (x+100-x-1):1+1=100(số hạng)
\(\Rightarrow\dfrac{\left(2x+101\right).100}{2}=5750\\ \Rightarrow2x+101=\dfrac{5750.2}{100}\\ \Rightarrow2x+101=115\\ \Rightarrow2x=14\\ \Rightarrow x=7\\ Vậy........\)
Câu 1:
a) 8 . 6 + 288 . (x + 3)2 = 50
\(\Rightarrow\) 48 + 288 . (x + 3)2 = 50
\(\Rightarrow\) 288 . (x + 3)2 = 2
\(\Rightarrow\) (x + 3)2 = \(\dfrac{1}{144}\)
\(\Rightarrow\) x + 3 = \(\pm\dfrac{1}{12}\)
\(\Rightarrow x=-2\dfrac{11}{12};-3\dfrac{1}{12}\)
b) (x + 1) + (x + 2) + (x + 3) + ... + (x + 100) = 5750
\(\Rightarrow\) 100x + (1 + 100) . 100 : 2 = 5750
\(\Rightarrow\) 100x + 5050 = 5750
\(\Rightarrow\) 100x = 700
\(\Rightarrow\) x = 7
