2Cos²x - 3Sinx = 0
Cos²x + Sin² = 1 => Cos²x = 1 - Sin²x
2(1 - Sin²x) - 3Sinx = 0
2 - 2Sin²x - 3Sinx = 0
-2Sin²x - 3Sinx + 2 = 0
2Sin²x + 3Sinx - 2 = 0
Sinx = t ∈ [-1;1]
2t² + 3t - 2 = 0
D = 9 - 4 * 2 * (-2) = 25
t₁ = (-3 + √25) / 4 = 1/2
t₂ = (-3 - √25) / 4 = -2 ∉ [-1;1]
Sinx = 1/2
x = π/6 + 2πn, n∈Z
x = 5π/6 + 2πn, n∈Z
( 50 - x)² = 20² + x²
2500 - 100x + x² = 400 + x²
x² - x² - 100x = 400 - 2500
- 100x = - 2100
100x = 2100
x = 21
Решение во вложении....................
=а^2+а-2-а^2+а+2=12
=k^2-k-2-k^2+k+30=28 чта и требовалось доказать