Question

Tìm \(x\):

\(\left(2x-1\right)^2-\left(x-2\right)^2-\left(x+2\right).\left(x-2\right)=4\)

Answer 1

(2x-1)²-(x-2)²-(x+2)(x-2)

=4x²-4x+1-x²+4x-4-x²+4

=4x²-2x²

=2x²

=>2x²=4

=>x=\(\sqrt{2}\)

Answer 2

( 2x - 1 )² - ( x - 2 )² - ( x + 2 ) . ( x - 2 ) = 4

=> 4x² - 4x + 1 - x² + 4x - 4 - x² + 4 = 4

=> 2x² + 3= 4

=> 2x² = 1

=> x² = 0,5

=> x = \(\sqrt{0,5}\) hoặc x = -\(-\sqrt{0,5}\)

Vậy x =\(\sqrt{0,5}\) ; x = -\(\sqrt{0,5}\)