Question

Tìm x \(\in\)N biết:

a)\(x^{10}\)\(=\)\(1^x\)

b)\(x^{10}=x\)

c)\(\left(2x-15\right)^5=\left(2x-15\right)^3\)

Answer 1

a./ \(\Leftrightarrow x^{10}=1\Leftrightarrow x=\pm1\)

b./ \(\Leftrightarrow x^{10}-x=0\Leftrightarrow x\left(x^9-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^9=1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)

c./ \(\Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\Leftrightarrow\left(2x-15\right)^3\left(\left(2x-15\right)^2-1\right)=0\Leftrightarrow\orbr{\begin{cases}2x-15=0\\\left(2x-15\right)^2=1\end{cases}}\)

2x - 15 = 0 \(\Leftrightarrow x=\frac{15}{2}\)2x - 15 = 1 \(\Leftrightarrow x=\frac{16}{2}=8\)2x - 15 = -1 \(\Leftrightarrow x=\frac{14}{2}=7\)

Answer 2

1^10=1^1

1^10=1

(2*8-15)^3=(2*8)^3

Ý c,x có thể bằng 7