a) (2/3) x² = 12 / * 3/2 x² = 12*(3/2) x² = 18 x = √18 = √9 *√2 = 3√2 --------------------------- b) x² - 7 x = 0 x*(x - 7) = 0 x = 0 lub x - 7 = 0 Odp. x = 0 lub x = 7 ---------------------------- c) (-1/2) x² = √(3x) , zakładamy, że 3x ≥ 0 <=> x ≥ 0 i podnosimy obustronnie do kwadratu (1/4) x⁴ = 3x / * 4 x⁴ = 12 x x⁴ - 12 x = 0 x*(x³ - 12) = 0 x = 0 lub x³ - 12 = 0 x = 0 lub x³ = 12 x = 0 lub x = ∛12 , ale ∛12 nie spełnia wyjściowego równania Odp. x = 0 ---------------------------------------------------------- d) x² - 7x = (1/2)*(8 - 14 x) x² - 7x = 4 - 7x x² = 4 Odp. x = -2 lub x = 2 ------------------------------------------------------------ e) x² = 4 i 1/6 x² = 25/6 Odp. x = - 5/√6 lub x = 5/√6 ---------------------------------------------------------- f) 5x + 4 x² = 2 x² - 3 x 4 x² - 2 x² +5x + 3 x = 0 2 x² + 8 x = 0 2x*(x + 4) = 0 x = 0 lub x + 4 = 0 Odp. x = 0 lub x = -4 ----------------------------------------------------------- g) (x -3)(x +2) = ( x +4)(2 - x) - 14 x² - 3x +2x - 6 = 2x - x² + 8 - 4x - 14 x² - x - 6 = - x² -2x - 6 2 x² + x = 0 x*(2x + 1) = 0 x = 0 lub 2x + 1 = 0 x = 0 lub 2x = -1 Odp. x = 0 lub x = -1/2 =====================================================
