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\(a,ĐK:x\le\dfrac{5}{3}\\ PT\Leftrightarrow-3x+5=49\\ \Leftrightarrow x=-\dfrac{44}{3}\left(tm\right)\\ b,ĐK:x\ge-12\\ PT\Leftrightarrow\dfrac{1}{2}x+6=2\\ \Leftrightarrow\dfrac{1}{2}x=-4\\ \Leftrightarrow x=-8\left(tm\right)\\ c,ĐK:x\ge-\dfrac{1}{2}\\ PT\Leftrightarrow2x+1=13+4\sqrt{3}\\ \Leftrightarrow x=\dfrac{12+4\sqrt{3}}{2}=6+2\sqrt{3}\left(tm\right)\\ d,PT\Leftrightarrow\left|3x-1\right|=8\Leftrightarrow\left[{}\begin{matrix}3x-1=8\\1-3x=8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{7}{3}\end{matrix}\right.\)
A = 12 - 22 + 32 - 42 + 52 - 62 + 72 - .......- 582 + 592
A = 12 + ( 32 - 22) + ( 52 - 42) + (72 - 62) +....+ ( 592 - 582)
A = 1 + ( 3-2)(2+3) + (5-4)(4+5) + (7-6)(6+7)+....+(59-58)(58+59)
A = 1 + 2 + 3 + 4 + 5 + 6 + 7 + ....+ 58 + 59
A = ( 59 + 1).{ (59 - 1): 1 + 1 } : 2
A = 1770
B = \(\dfrac{2^{2016}-2^{2015}+2^{2014}-2^{2013}+2^{2012}-2^{2011}+2^{2010}-2^{2009}}{2^{2008}}\)
Đặt tử số là A
ta có
A = 22016 - 22015+22014 - 22013 + 22012 - 22011 + 22010- 22009
2 A= 22017- 22016 + 22015- 22014 +22013-22012 + 22011 - 22010
2A + A = 22017 - 22009
3A = 22017 - 22009
A = (22017 - 22009):3
B = A : 8 = (22017- 22009) : 3 : 8
B = (22017 - 22009) : 24
\(a,\sqrt{3^2}-\sqrt{\left(-7\right)^2}+\sqrt{\left(-1\right)^2}\)
\(=3-7+1\)
\(=-3\)
\(b,-2\sqrt{\left(-2\right)^2}+3\sqrt{\left(-5\right)^2}+\sqrt{3^2}\)
\(=-2.2+3.5+3\)
\(=-4+15+3\)
\(=14\)
\(c,\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(2+\sqrt{2}\right)^2}\)
\(=\left|2-\sqrt{2}\right|+\left|2+\sqrt{2}\right|\)
\(=2-\sqrt{2}+2+\sqrt{2}\)
\(=4\)
\(d,\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(=\left|3-\sqrt{2}\right|-\left|1-\sqrt{2}\right|\)
\(=3-\sqrt{2}-\left(-1+\sqrt{2}\right)\)
\(=3-\sqrt{2}+1-\sqrt{2}\)
\(=-2\sqrt{2}+4\)