Question

Bài 1: Tính hợp lý:

a. 1152 - (374 + 1152) + (374 - 65)

b. \(\dfrac{7}{12}\) + \(\dfrac{5}{6}\) + \(\dfrac{1}{4}\) - \(\dfrac{3}{7}\) - \(\dfrac{5}{12}\)

c. \(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)

d, \(\dfrac{3}{2^2}\) . \(\dfrac{8}{3^2}\) . \(\dfrac{15}{4^2}\) ... \(\dfrac{899}{30^2}\)

Bài 2: Tìm x biết:

a, 2^x + 2^x+1 + 2^x+2 + 2 ^x+3 = 480

b, \(\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\right)\) . x = \(\dfrac{2012}{1}+\dfrac{2011}{2}+\dfrac{2010}{3}+...+\dfrac{2}{2011}+\dfrac{1}{2012}.\)

Answer 1

Bài 1 : Tính hợp lý : c. \(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\) = \(\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\) = \(\dfrac{3^{29}.\left(11-3\right)}{2^2.3^{28}}\) = \(\dfrac{3^{29}.2^3}{2^2.3^{28}}\) = 6

Answer 2

Bài 1: Tính hợp lý:

d. \(\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}...............\)\(\dfrac{899}{30^2}\) = \(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}..............\dfrac{29.31}{30.30}\) = \(\dfrac{1.2.3.....29}{2.3.4.....30}.\dfrac{3.4.5.....31}{2.3.4.....30}\) = \(\dfrac{1}{30}.\dfrac{31}{2}\) = \(\dfrac{31}{60}\)

Answer 3

Bài 2: Tìm x biết:

a, \(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\) \(\Rightarrow\) \(2^x.\left(1+2+2^2+2^3\right)=480\) \(\Rightarrow\) \(2^x.15=480\) \(\Rightarrow\) \(2^x=480:15\) \(\Rightarrow\) \(2^x=32\) \(\Rightarrow\) \(2^x=2^5\) \(\Rightarrow\) \(x=5\)

Answer 4

1.Tính hợp lý:

a. 1152 - (374 + 1152) + (374 - 65) = 1152 - 374 - 1152 + 374 - 65 = ( 1152 - 1152 ) + ( -65) + ( 374 - 374 ) = 0 + ( - 65) + 0 = -65

Answer 5

Bài 1: Tính hợp lý:

b. \(\dfrac{7}{12}+\dfrac{5}{6}+\dfrac{1}{4}-\dfrac{3}{7}-\dfrac{5}{12}\) = \(\left[\left(\dfrac{7}{12}-\dfrac{5}{12}\right)+\dfrac{5}{6}\right]+\dfrac{1}{4}-\dfrac{3}{7}\) = \(\left(\dfrac{1}{6}+\dfrac{5}{6}\right)+\dfrac{1}{4}-\dfrac{3}{7}\) = \(1+\dfrac{1}{4}-\dfrac{3}{7}\) = \(\dfrac{5}{4}-\dfrac{3}{7}\) = \(\dfrac{23}{28}\)