Объяснение:
220. Выделим квадрат двучлена:
=a) 2x²−3x + 7 = 2(x³²− 2¹ x + x+ 3 7 2 GOZP2MA.INFO
GUZPUTINA.INFO
GUZPU
GOZPU
GUZPU
GOZPU
= 2(x²-2·x· ²³ +₁ + 27/2 = - 2((x-2²-47)=2(x-2)²2-5² ². 3 9 9 4 16 16 2 GOZPUTINA.INFO 16 GUZPUTINA.INFO
4 -ó) −3x² + 4x−1 = −3(x² - ²x + x + — — ) = −3(x³²-2.x. GD + 4 4 - —— +-) 99 3
= -3((x - ²)²) = -3(x-²)² + 3 GUZE 9 MA
GUZPUTINA.INFO
GUZPUTINA.IN −b) 5x²-3x = 5(x²_²_x) = S(x = 5(x²-2x. GOZPUTINA.INFO 3 9 9 + ) = 5((x—_²_) ²__ 9 100 GOZPUTINA.INFO
GOZPUTINA.INFO 10 20
GOZPUTINA.INFO
r) -4x² + 8x = 4(x²-2x) = -4(x²-2·x·1+1−1) = -4((x-1)²-1) = -4(x-1)² + 4.
а) z* = -z·i
z = x + iy
x - iy = -(x + iy)·i
x - iy = -ix + y
x + ix = y + iy
x·(1 + i) = y·(1 + i)
y = x
z = x + ix, x ∈ R
б) 2·|z| - 8z + 1 + 2i = 0
z = x + iy
2√(x² + y²) - 8·(x + iy) + 1 + 2i = 0
2√(x² + y²) - 8x - i8y + 1 + 2i = 0
2√(x² + y²) = (8x - 1) + i(8y - 2)
2√(x² + y²) = 8x - 1
8y - 2 = 0
y = 1/4
2√(x² + (1/4)²) = 8x - 1
4(x² + 1/16) = 64x² - 16x + 1
8x - 1 ≥ 1/2
4x² + 1/4 = 64x² - 16x + 1
8x ≥ 3/2
60x² - 16x + 3/4 = 0
x ≥ 3/16
240x² - 64x + 3 = 0
D = 64² - 4·240·3 = 1216
x = (64 (+/-) √1216)/480 = (64 (+/-) 8√19)/480 = (8 (+/-) √19)/60
x = 2/15 (+/-) √19/60
x ≥ 3/16
x = 2/15 + √19/60
z = 2/15 + √19/60 + i/4
