Question

\(x ( x − 1 ) + x ( x + 1 ) + ( x − 1 ) ( x + 1 ) = 242\)

Answer 1

\(x\left(x-1\right)+x\left(x+1\right)+\left(x-1\right)\left(x+1\right)=242\)

\(\Rightarrow x^2-x+x^2+x+x^2-1=242\)

\(\Rightarrow3x^2=243\)

\(\Rightarrow x^2=81\)

\(\Rightarrow x=\pm9\)

Answer 2

\(x ( x − 1 ) + x ( x + 1 ) + ( x − 1 ) ( x + 1 ) = 242\)

`=> x ( x -1 + x + 1 ) + ( x^2 - 1) = 242`

`=> x ( 2x ) + ( x^2 - 1) = 242`

`=> 2x^2 + x^2 - 1 = 242`

`=> 3x^2 = 242 + 1`

`=> 3x^2 = 243`

`=> x^2 = 243 : 3`

`=> x^2 = 8 1`

`=> x = 9^2`

`=> x = (-9)^2`

`=> x = 9 ` hoặc `x = - 9`

Vậy `x in {9; -9}`