Question

(x+1)²+(2x-3)²=(2x-4)²+(x-6)²​

Answer 1

( x + 1 )² + ( 2x - 3 )² = ( 2x - 4 )² + ( x - 6 )²​

( x + 1 )² = x² + 2x + 1

( 2x - 3 )² = 4x² - 12x + 9

( 2x - 4 )² = 4x² - 16x + 16

( x - 6 )² = x² - 12x + 36

x² + 2x + 1 + 4x² - 12x + 9 = 4x² - 16x + 16x + x² - 12x + 36

2x + 1 + 4x² - 12x + 9 = 4x² - 16x + 16 - 12x + 36

2x + 1 - 12x + 9 = - 16x + 16 - 12x + 36

2x + 1 + 9 = - 16x + 16 + 36

2x + 10 = - 16x + 16 + 36

2x + 10 = - 16x + 52

2x + 16x = 52 - 10

18x = 42

x = 42/18 simplificăm prin 6 ⇒ x = 7/3

Answer 2

$(x+1)^2+(2x-3)^2 = (2x-4)^2+(x-6)^2\\\\(x+1)^2-(x-6)^2 = (2x-4)^2 - (2x-3)^2 \\\\ \\\Big[(x+1)-(x-6)\Big]\Big[(x+1)+(x-6)\Big] =\\\\= \Big[(2x-4)-(2x-3)\Big]\Big[(2x-4)+(2x-3)\Big]\\ \\\\ 7\cdot (2x-5) = (-1)\cdot(4x-7) \\ \\ 14x-35 = -4x+7 \\ \\ 18x = 42 \\ \\ 3x = 7 \\ \\ \Rightarrow \boxed{x= \dfrac{7}{3}}$