Cho x = - 98; a = 61; m = - 25
Tính giá trị biểu thức sau
a) x + 8 - x - 22
b) -x - a + 12 + a
c) -m + 7 + m - 8
d) m - 24 - x + 24 + x
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Ta có\(M=\left[\left(1+\frac{1}{98}\right)+\left(\frac{1}{2}+\frac{1}{97}\right)+...+\left(\frac{1}{49}+\frac{1}{50}\right)\right].2.3...98\)
\(=\left[\frac{99}{1.98}+\frac{99}{2.97}+...+\frac{99}{49.50}\right].2.3...98=99\left(\frac{1}{1.98}+\frac{1}{2.97}+...+\frac{1}{49.50}\right).2.3...98\)
\(=99\left(\frac{k_1+k_2+...+k_{49}}{1.2.3...98}\right).2.3...98\left(k_1,k_2...k_{49}\varepsilonℕ^∗\right)=99\left(k_1+k_2+...+k_{49}\right)⋮99\Rightarrow M⋮99\left(đpcm\right)\)
98 x a + b x 98 - c x 98 = 98 x (a+b-c) = 98 x 160 = 15680
\(x\times98+x:0,5=2017\)
\(x\times98+x\times2=2017\)
\(x\times\left(98+2\right)=2017\)
\(x\times100=2017\)
\(x=2017:100\)
\(x=20,17\)
\(\frac{x-1}{99}+\frac{x-2}{98}+\frac{x-3}{97}+\frac{x-4}{96}=4\)
\(\Leftrightarrow\left(\frac{x-1}{99}+\left(-1\right)\right)+\left(\frac{x-2}{98}+\left(-1\right)\right)+\left(\frac{x-3}{97}+\left(-1\right)\right)+\left(\frac{x-4}{96}+\left(-1\right)\right)=0\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{98}+\frac{x-100}{97}+\frac{x-100}{96}=0\)
\(\Leftrightarrow\left(x-1\right).\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
Cho x = - 98; a = 61; m = - 25.
a) x + 8 - x - 22.
= (-98) + 8 - (-98) - 22
= (-90) + 98 - 22
= 8 - 22
= - 14.
b) -x - a + 12 + a
= -(-98) - 61 + 61
= 98 + ( 61 - 61)
= 98 + 0
= 98.
c) -m + 7 + m - 8
= -(-25) + 7 + (-25) - 8
= [25 + (-25)] + 7 - 8
= 0 + 7 - 8
= -1.
d) m - 24 - x + 24 + x
= (-25) - 24 -(-98) + 24 + (-98)
= (-25) - 24 + 98 + 24 - 98
=(-25) + [(24 - 24) + ( 98 - 98)
= -25.