Question

1. Tính : 2019^{(1000-1^2).(1000-2^2).....(1000-15^2)}

2. Tính : \(\frac{\left(5^4-5^3\right)^3}{125^4}\)

3. Tìm x,y biết: \(\text{( 2x- 5)}^{2018}+\left(3y+4\right)^{2018}=0\)

giúp tớ với đang cần gấp lắm!

Answer 1

3.

\(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2018}=0\)

Ta luôn có: \(\left(2x-5\right)^{2018}\ge0\forall x;\left(3y+4\right)\ge0\forall y\)

Mà \(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2018}=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left(2x-5\right)^{2018}=0\\\left(3y+4\right)^{2018}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x-5=0\\3y+4=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=5\\3y=-4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\frac{5}{2}\\y=\frac{-4}{3}\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(\frac{5}{2};\frac{-4}{3}\right)\)