Question

Tính giá trị của biểu thức:

a)\(2\dfrac{1}{547}\).\(\dfrac{3}{211}\)-\(\dfrac{546}{547}\).\(\dfrac{1}{211}\)-\(\dfrac{4}{547.211}\)

b)x¹⁵-8x¹⁴+8x¹³-8x¹²+...-8x²+8x-5 với x=7

c)\(2\dfrac{1}{315}\).\(\dfrac{1}{651}\)-\(\dfrac{1}{105}\).\(3\dfrac{650}{651}\)-\(\dfrac{4}{315.651}\)+\(\dfrac{4}{105}\)

Answer 1

a: \(=\dfrac{\left(2\cdot547+1\right)\cdot3}{547\cdot211}-\dfrac{546}{547\cdot211}-\dfrac{4}{547\cdot211}\)

\(=\dfrac{2735}{547\cdot211}=\dfrac{5}{211}\)

b: x=7 nên x+1=8

\(x^{15}-8x^{14}+8x^{13}-8x^{12}+...-8x^2+8x-5\)

\(=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-x^{12}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-5\)

\(=x^{15}-x^{15}-x^{14}+x^{14}-...-x^3-x^2+x^2+x-5\)

=x-5=7-5=2