Можете помочь 4,5 задание. Created by ваня2546. algebra-ru

Можете помочь 4,5 задание...

ваня2546 @ваня2546

August 2022 1 1 Report

Можете помочь 4,5 задание

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sharadi

Verified answer

4) Sin⁴x + Cos⁴x + Sin2x = 7/5
(Sin²x)² + Cos⁴x + Sin2x = 7/5
(1 - Cos²x)² + Cos⁴x + Sin2x = 7/5
1 - 2Cos²x + Cos⁴x +Cos⁴x + Sin2x = 7/5
-2Cos²x +2Cos⁴x + Sin2x = 2/5
-2Cos²x +2Cos⁴x +2SinxCosx = 2/5
-Cos²x +Cos⁴x +SinxCosx  = 1/5
-Cos²x(1 - Cos²x) + SinxCosx = 1/5
-Cos²xSin²x + SinxCosx = 1/5 |*4
-4Cos²xSin²x + 2*2SinxCosx = 4/5
-Sin²2x +2Sin2x = 4/5 |*5
-5Sin²2x + 10Sin2x -4 = 0
Sin2x = t
-5t² + 10t - 4 = 0
5t² -10t +4 = 0
t = (5+-√(25 -20))/5
t₁ = (5+√5)/5= 1 + √5/5 t₂= 1 - √5/5
Sin2x =  1 + √5/5 Sin2x =  1 - √5/5
∅     2x = (-1)^n arcSin (1 - √5/5) + nπ, n ∈Z
x =  (-1)^n arcSin(1 - √5/5)/2+ nπ/2, n ∈Z
5) (х² -х +1)⁴ - 5х²(х² -х +1)² + 4х⁴ = 0
(х² - х +1)² = t
t² - 5x² t + 4x⁴ = 0
D = b² -4ac = 25x⁴ - 16x⁴ = 9x⁴
t₁= (5x² + 3x²)/2 = 4x² t₂ = (5x² - 3x²)/2 = х²
(х² - х +1)² = t
(х² - х +1)² = 4х²     (х² - х +1)² = х²
а)х²-х +1 = 2х б)  х² -х +1 = -2х в) х² -х +1 = х г) х² -х +1 = -х
х² -3х +1 = 0     х² +х +1 = 0 х²-2х +1 =0 х² +1 = 0
D = 5 D = -3 (x-1)² =0   x² = -1
x = (3 +-√5)/2   ∅ х = 1 ∅
Ответ: x = (3 +-√5)/2
х = 1

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