Cho x = -98; a = 61; m = -25
Rút bọn các biểu thức rồi tính giá trị
a) x + 8 - x - 22
b) -x - a + 12 + a
c) a - m + 7 + m - 8
d) m - 24 - x + 24 + x*
Giúp mk nha ...mai đi học rồi <3 <3 <3 Cảm ơn
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Ta có:
$A=\dfrac{1+(1+2)+(1+2+3)+\cdots+(1+2+\cdots+98)}{1\times98+2\times97+3\times96+\cdots+98\times1}$
Tử số:
$1+(1+2)+(1+2+3)+\cdots+(1+2+\cdots+98)$
$=1+2+2^2+?$
Cách dễ nhất là viết:
$1+2+\cdots+k=\dfrac{k(k+1)}2$
Nên tử số:
$=\dfrac{1\cdot2}{2}+\dfrac{2\cdot3}{2}+\cdots+\dfrac{98\cdot99}{2}$
$=\dfrac{1}{2}(1\cdot2+2\cdot3+\cdots+98\cdot99)$
$=\dfrac{1}{2}\cdot\dfrac{98\cdot99\cdot100}{3}$
$=161700$
Mẫu số:
$1\cdot98+2\cdot97+3\cdot96+\cdots+98\cdot1$
$=1(99-1)+2(99-2)+\cdots+98(99-98)$
$=99(1+2+\cdots+98)-(1^2+2^2+\cdots+98^2)$
$=99\cdot\dfrac{98\cdot99}{2}-\dfrac{98\cdot99\cdot197}{6}$
$=161700$
Do đó:
$A=\dfrac{161700}{161700}=1$
Vậy $A=1$.
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
\(x\times98+x:0,5=2017\)
\(x\times98+x\times2=2017\)
\(x\times\left(98+2\right)=2017\)
\(x\times100=2017\)
\(x=2017:100\)
\(x=20,17\)
\(\frac{x-1}{99}+\frac{x-2}{98}+\frac{x-3}{97}+\frac{x-4}{96}=4\)
\(\Leftrightarrow\left(\frac{x-1}{99}+\left(-1\right)\right)+\left(\frac{x-2}{98}+\left(-1\right)\right)+\left(\frac{x-3}{97}+\left(-1\right)\right)+\left(\frac{x-4}{96}+\left(-1\right)\right)=0\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{98}+\frac{x-100}{97}+\frac{x-100}{96}=0\)
\(\Leftrightarrow\left(x-1\right).\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{97}+\frac{1}{96}\right)=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
a , x + 8 - x - 22
= ( x - x ) + 8 - 22
= 0 - 14 = - 14
b , - x - a + 12 + a
= ( a - a ) - x + 12
= 0 - x + 12
= - 98 + 12 = -86
c , a - m + 7 + m - 8
= - m + m + a + 7 - 8
= 0 + a - 1
= 61 - 1 = 60
d , m - 24 - x + 24 + x
= ( - 24 + 24 ) - x + x + m
= 0 + 0 - 25 = - 25
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.