Rozwiaz rownania: a) x² + 3x-10=0 b) (x-3)²-2x=4x+25 c) x4 -5x²+4=0

a) x² + 3x-10=0 Δ = 9 + 40 Δ = 49 √Δ = 7 x1 = -2 - 7/2 x1 = - 9/2 x1 = - 4,5 x2 = -2 + 7/2 x2 = 2,5 b) (x-3)²-2x=4x+25 x² - 6x + 9 - 2x - 4x - 25 = 0 x² - 12x - 16 = 0 Δ = 144 + 64 Δ = 208 √Δ = 4√13 x1 = 12 + 4√13/2 x1 = 6 + 2√13 x2 = 12 - 4√13/2 x2 = 6 -2√13 c) x4 -5x²+4=0 -5x² + 4x + 4 = 0 Δ = 16 + 80 Δ = 96 √Δ = √96 √Δ = 4√6 x1 = -4 - 4√6/-2 x1 = 2√6 x2 = -4 + 4√6/-2 x2 = -2√6

Rozwiaz rownania: a) x² + 3x-10=0 Δ = 3² -4*1*(-10) = 9 +40 = 49 √Δ = √49 = 7 x1 = ( -3 -7):2*1 = (-10):2 = -5 x2 = ( -3 +7) : 2*1 = 4 : 2 = 2 b) (x-3)²-2x=4x+25 x² - 6x + 9 -2x -4x -25 = 0 x² -10x - 16 = 0 Δ = (-10)² -4*1*(-16)= 100 + 64 = 164 √Δ = √164 = √4*√41 = 2√41 x1 = [-(-10) -2√41 ] : 2*1 = ( 10 -2√41 ) :2 = 5 -√41 x2 = [-(-10) +2√41 ] : 2*1 = ( 10 +2√41 ) :2 = 5 +√41 c) x⁴ -5x²+4=0 x² = t t² - 5t +4 = 0 Δ = (-5)² -4*1*4 = 25 -16 = 9 √Δ = √9 = 3 t1 = [-(-5)-3] : 2*1 = (5 -3): 2 = 2 :2 = 1 t2 = [-(-5)+3] : 2*1 = (5 +3): 2= 8 :2 = 4 x² = 1 lub x² = 4 x² -1 = 0 (x -1)(x+1) = 0 x = 1 lub x = -1 lub x² = 4 x² -4 = 0 (x -2)(x +2) = 0 x = 2 lub x = -2 Odp. x = 1 lub x = -1 lub x = 2 lub x = -2

odpowiedź w załączniku :)