a) [latex](2x+7)^2 + 5 = (2x-3)(2x+3)+7[/latex] [latex]4x^2 + 28x + 49 + 5 = 4x^2 - 9 + 7[/latex] [latex]4x^2 + 28x + 54 = 4x^2 - 2[/latex] [latex]4x^2 + 28x - 4x^2 = - 2 - 54[/latex] [latex]28x = - 56 /:28 [/latex] [latex]x = - 2[/latex] Sprawdzenie: (2x + 7)² + 5 = (2x - 3)(2x + 3) + 7 [2·(- 2) + 7]² + 5 = [2·(- 2) - 3][2·(- 2) + 3] + 7 (- 4 + 7)² + 5 = (- 4 - 3)(- 4 + 3) + 7 3² + 5 = - 7 · ( - 1) + 7 9 + 5 = 7 + 7 14 = 14 b) [latex](x+frac{1}{2})^2 - (x-1)(x+1) = 16[/latex] [latex]x^2 + x + frac{1}{4} - x^ 2 + 1 = 16[/latex] [latex]x + 1frac{1}{4} = 16[/latex] [latex]x = 16 - 1frac{1}{4}[/latex] [latex]x = 14frac{3}{4}[/latex] Sprawdzenie: (x + ½)² - (x - 1)(x + 1) = 16 (14¾ + ½)² - (14¾ - 1)(14¾ + 1) = 16 (⁵⁹/₄ + ²/₄)² - 13¾ · 15¾ = 16 (⁶¹/₄)² - ⁵⁵/₄ · ⁶³/₄ = 16 ³⁷²¹/₁₆ - ³⁴⁶⁵/₁₆ = 16 ²⁵⁶/₁₆ = 16 16 = 16 c) [latex]- (x - 4)^2 = (3 - x)(3 + x)[/latex] [latex]-x^2 + 8x - 16 = 9 - x^2[/latex] [latex]-x^2 + 8x + x^2 = 9 + 16[/latex] [latex]8x = 25 /:8[/latex] [latex]x = frac{25}{8}[/latex] [latex]x = 3frac{1}{8}[/latex] Sprawdzenie: - (x - 4)² = (3 - x)(3 + x) - (3⅛ - 4)² = (3 - 3⅛)(3 + 3⅛) - (- ⅞)² = - ⅛ · 6⅛ - ⁴⁹/₆₄ = - ⅛ · ⁴⁹/₈ - ⁴⁹/₆₄ = - ⁴⁹/₆₄
