M³+n³=(m+n)(m²-mn+n²)
125+n³=(5+n)(25-5n+n²)
1/125m³-27=(1/5m-3)(1/25m²+3/5m+9)
27n³-64m³=(3n-4m)(9n²+12mn+16m²)
2m = 1024
m = 1024/2
m = 512
<span>вычислить (√(2) + i√(2))⁵ ˣ (i -√(3))⁹
Решение
В алгебраической форме
</span>(√(2)+i √(2)) =√2(1+i)
(√(2)+i √(2))² = (√2(1+i))² = 2(1 + 2i + i²) = 2(1 + 2i -1) =<span> 4i </span>
(√(2)+i √(2))⁴ = ((√(2)+i √(2))²)² = (<span>4i)² =16i² = -16
</span>
(√(2)+i √(2))⁵ = (√(2)+i √(2))⁴ *((√(2)+i √(2)) = -16*√2(1+i) =-16√2(1+i)
(i - √(3))² = i² - 2<span>√(3)i + 3 = </span><span>-1 - 2√(3)i + 3 = </span><span>2 - 2√(3)i =</span><span><span><span><span> 2(1 -√(3)i)</span></span></span></span>
(i - √(3))⁴ = ((i - √(3))²)² = (<span><span>2(1 - √(3)i)</span>)² = 4(1 - 2</span><span>√(3)i + 3i²)= </span><span>4(1 - 2<span>√(3)i - 3)=
=</span></span><span> 4(-2 - 2<span>√(3)i) = -8(1 + </span></span><span><span><span>√(3)i) </span></span></span>
(i - √(3))⁸ = ((i - √(3))⁴)² = (-8(1 + <span>√(3)i))² = 64(1 + 2</span><span>√(3)i + 3i²) =
= 64(1 +2√(3)i - 3) = 64(-<span>2 + 2√(3)i) = -128(1 - </span>√(3)i) </span>
(i - √(3))⁹ = (i - √(3))⁸* (i - √(3))= <span> -128(1 - √(3)i)* </span>(i - √(3)) =
= -128(<span>i - √(3) -</span><span>√(3)i² + 3i) = </span><span><span>-128(i - √(3) +-<span>√(3) + 3i) = -128*4i =-512i</span></span> </span>
(√(2) + i√(2))⁵ ˣ (i -√(3))⁹ = -16√2(1+i)* (-512i) = 8192√2(i + i²) =
= 8192√2(-1 + i) = -8192√2 + 8192√2i
Ответ:-8192√2 + 8192√2i
Пошаговое объяснение:
Задача 1.
b1 = 10, 10*2 = 20 = b2 , 20*2 = 40 = b3 ,
40*2 = 80 = b4 - ответ
Задача 2.
q = b2/b1 = -35 : -7 = +5
b3 = b2*q = - 35*5 = - 175 = b3 - ответ.
Задача 3. Сумма S5
Решение.
S(n) =b₁*(1-qⁿ))/(1-q)
qⁿ = (1/2)^5 = 1/32
1 - q = 1.5
S5 = 64*(33/32)/(3/2) = 44
S5 = 44 - сумма пяти членов - ответ
Проверка. 64 -32+16 -8 + 4 = 44 - правильно