Question

Tìm x,y thuộc N:

a) x + (x + 1) + (x + 2) + (x + 3) + ... + (x + 30) = 1240

b) 2 . |x - 1|² - 3 = 5

Answer 1

a)x + (x + 1) + (x + 2) + (x + 3) + ... + (x + 30) = 1240

\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+...+30\right)=1240\)

\(\Leftrightarrow31x+465=1240\)

\(\Leftrightarrow31x=775\Leftrightarrow x=25\)

b)2|x - 1|² - 3 = 5

\(\Leftrightarrow2\left(x-1\right)^2=8\)

\(\Leftrightarrow\left(x-1\right)^2=4\)

\(\Leftrightarrow\left(x-1\right)^2=2^2=\left(-2\right)^2\)

\(\Leftrightarrow x-1=\pm2\)

Xét x-1=2 =>x=3Xét x-1=-2 =>x=-1

Answer 2

về việc đổi |x-1|² thành (x-1)² khá đơn giản

|x-1|>=0 =>|x-1|^2>=0

(x-1)^2>=0