Question

a)\(\left(x^4\right)^3=\dfrac{x^{15}}{x^5}\)

b)\(2^x+2^{x+3}=144\)

c)Biết rằng \(1^2+2^2+3^2+....+10^2=385\) hãy tính tổng sau đây

S=\(100^2+200^2+300^2+....+1000^2\)

Answer 1

a)Có: (x⁴)³=\(\dfrac{x^{15}}{x^5}\)

<=> x¹²=x¹⁰

<=> x¹²-x¹⁰=0

<=> x¹⁰(x²-1)=0

<=> \(\left[{}\begin{matrix}x^{10}=0\\x^2-1=0\end{matrix}\right.\)<=>\(\left[{}\begin{matrix}x=0\\x^2=1\end{matrix}\right.< =>\left[{}\begin{matrix}x=0\\x\in\left\{1;-1\right\}\end{matrix}\right.\)

Vậy x\(\in\left\{1;-1;0\right\}\)

b)Có 2^x+2^x+3=144

<=> 2^x(1+2³⁾=144

<=> 2^x=16=2⁴

=> x=4

c) Có \(1^2+2^2+3^2+...+10^2=385\)

<=> \(100^2\left(1^2+2^2+3^2+...+10^2\right)=385.100^2\)

<=> \(100^2.1^2+100^2.2^2+...+100^2.10^2=3850000\)

<=> \(100^2+200^2+...+1000^2=3850000\)