Question

(x-1)^2010-(2y-6)^2012=0

Answer 1

\(\left(x-1\right)^{2010}-\left(2y-6\right)^{2012}=0\)

\(Do:\left(x-1\right)^{2010}\ge0;\left(2y-6\right)^{2012}\ge0\)

\(\Rightarrow\left(x-1\right)^{2010}=0\Rightarrow x-1=0\Rightarrow x=1\)

\(\Rightarrow\left(2y-6\right)^{2012}=0\Rightarrow2y-6=0\)\(\Rightarrow2y=6\Rightarrow y=\dfrac{6}{2}=3\)

Vậy \(x=1;y=3\)

Answer 2

Vì (x-1)²⁰¹⁰ và (2y-6)²⁰¹² = 0

Nên (x-1)²⁰¹⁰ và (2y-6)²⁰¹² \(\ge\) 0

\(\Rightarrow\) (x-1)²⁰¹⁰ = 0

\(\Rightarrow\) (x-1)²⁰¹⁰ = 0²⁰¹⁰

\(\Rightarrow\) x - 1 = 0

x = 0 + 1

x = 1

\(\Rightarrow\) (2y-6)²⁰¹² = 0

\(\Rightarrow\) (2y-6)²⁰¹² = 0²⁰¹²

\(\Rightarrow\) 2y - 6 = 0

\(\Rightarrow\) 2y = 0 + 6

\(\Rightarrow\) 2y = 6

\(\Rightarrow\) y = 6 : 2

y = 3

Vậy x = 1; y = 3

Answer 3

(x-1)^2010-(2y-6)^2012=0

=> (x-1)^2010 =0 hoặc (x-1)^2010 =1

=> x-1=0

=> x=1

hoặc (x-1)^2010 =1

=> x-1=1

=> x=2

Và (2y-6)^2012 =0

=> 2y-6=0

=> 2y=6

=> y=3