Question

[đoraemon]

1)tìm x

a)(x-2)² =1

b)(2x-1)=-8

c)\(\left(x-\dfrac{2}{9}\right)\)⁶

d)(x-1)^x+2=(x-1)^x+4

^{2)tính giá trị biểu thức}

^{a) \(\dfrac{45^{10}\cdot5^{10}}{75^{10}}\)}

b)\(\dfrac{2^{15}\cdot9^4}{6^6\cdot8^3}\)

c)\(\dfrac{14^{16}\cdot21^{32}\cdot35^{48}}{10^{16}\cdot15^{32}\cdot7^{96}}\)

đ)(1000-1³)(1000-2³)(1000-3³)..........(1000-50³)

giúp mình nhé mai nộp gòi!

Answer 1

[Miko]

1. a) (x-2)² =1

=> x - 2 = \(\pm\sqrt{1}\)

=> x - 2 = 1 hoặc -1

=> x = 3 hoặc 1

b) 2x - 1= -8

=> 2x = -7

=>x = \(\dfrac{-7}{2}\)

c)thiếu đề

d) (x-1)^x+2 = (x-1)^x+4

(x-1)^x+2 = (x-1)^x+2+2

(x-1)^x+2 = (x-1)^x+2. (x-1)²

(x-1)^x+2 - (x-1)^x+2. (x-1)² = 0

=> (x-1)^x+2. [1 - (x-1)²] = 0

\(\left[{}\begin{matrix}\left(x-1\right)^{x+2}=0\\1-\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-1=0\\x-1=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

2a) \(\dfrac{45^{10}.5^{10}}{75^{10}}\) = \(\dfrac{\left(3.3.5\right)^{10}.5^{10}}{\left(5.5.3\right)^{10}}\) = \(\dfrac{3^{10}.3^{10}.5^{10}.5^{10}}{5^{10}.5^{10}.3^{10}}\) = \(3^{10}\)

b) \(\dfrac{2^{15}.9^4}{6^6.8^3}\)=\(\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}\)=\(\dfrac{2^{15}.3^8}{2^6.3^6.2^9}\)=\(3^2\)

Answer 2

[đoraemon]

c)\(\left(x-\dfrac{2}{9}^3\right)=\left(\dfrac{2}{3}\right)^6\)thank nhé