Tìm x biết
a) |x+2|-(-23)=-13
b)|x|+|y+1|=0
c)|+2|+y²=0
d)|-x|-(-11)=15
e)|x-1|-23=-17
g) 5-|x+5|=22
f)-37-|7-x|=-3
i) -7+|x-4|=-3
l) 9≤|x-1|<11
n) x-{57-(-42 +|-23-x|)}=13-{47+[25-(32-x)]
m)|x|+|y-1|=0 (|x|>0
Giúp mình với mai mình phải nộp r:(((
Đáp án:
n) \(\left[ \begin{array}{l}
x = \dfrac{{53}}{3}\\
x = 99
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {x + 2} \right| + 23 = – 13\\
\to \left| {x + 2} \right| = – 10\left( {vô lý} \right)\\
Do:\left| {x + 2} \right| \ge 0\forall x \in R
\end{array}\)
⇒ Phương trình vô nghiệm
\(\begin{array}{l}
b)\left| x \right| + \left| {y + 1} \right| = 0\\
\to \left[ \begin{array}{l}
x = 0\\
y = – 1
\end{array} \right.\\
c){y^2} + 2 = 0\\
\to {y^2} = – 2\left( l \right)
\end{array}\)
\(\begin{array}{l}
d)\left| x \right| = 4\\
\to \left[ \begin{array}{l}
x = 4\\
x = – 4
\end{array} \right.\\
e)\left| {x – 1} \right| = 5\\
\to \left[ \begin{array}{l}
x – 1 = 5\\
x – 1 = – 5
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 6\\
x = – 4
\end{array} \right.\\
g)\left| {x + 5} \right| = – 17\left( l \right)\\
\to x \in \emptyset \\
f)\left| {7 – x} \right| = – 34\left( l \right)\\
\to x \in \emptyset \\
i)\left| {x – 4} \right| = 4\\
\to \left[ \begin{array}{l}
x – 4 = 4\\
x – 4 = – 4
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 8\\
x = 0
\end{array} \right.\\
l)9 \le \left| {x – 1} \right| < 11\\
\to \left[ \begin{array}{l}
9 \le x – 1 < 11\\
– 9 \ge x – 1 > – 11
\end{array} \right.\\
\to \left[ \begin{array}{l}
10 \le x < 12\\
– 8 \ge x > – 10
\end{array} \right.\\
n)x – \left( {57 + 42 + \left| {x + 23} \right|} \right) = 13 – \left( {47 + 25 – 32 + x} \right)\\
\to x – 99 + \left| {x + 23} \right| = – 27 – x\\
\to \left| {x + 23} \right| = 76 – 2x\\
\to \left[ \begin{array}{l}
x + 23 = 76 – 2x\\
x + 23 = – 76 + 2x
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = 53\\
x = 99
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{{53}}{3}\\
x = 99
\end{array} \right.
\end{array}\)