Question

Rozwiaz rownania:

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

Answer 1

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

Answer 2

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

Answer 3

Odpowiedź w załączniku :)