§ 32: 32.38 (1)

32.38 Розв’яжіть рівняння:

1) 3-х • cosπx = 0;

3-х = 0; x = 3; x = 3;

cosπx = 0; πx = π2 + πn, n ∈ Z; x = 12 + n, n ∈ Z;

3 – x ≥ 0; x ≤ 3; x ≤ 3;

x = 3; x = 3; x = 3;

x = 12 + n, n ∈ Z; x = 12 + n, n ∈ Z; x = 12 + n, n ∈ Z;

12 + n ≤ 3; n ≤ 2,5 n ≤ 2.

Відповідь: x = 3; x = 12 + n, n ≤ 2, n ∈ Z.

2) 49-4x2 (sinπx + 3cosπx2) = 0;

49-4x2 = 0; 49 – 4x² = 0;

sinπx + 3cos πx2 = 0; 2sinπx2 • cosπx2 + 3cosπx2 = 0;

49 – 4x² ≥ 0; (7 – 2x)(7 + 2x) ≥ 0;

x = ± 72; x = ± 72;

2cosπx2(sin πx2 + 1,5) = 0; πx2 = π2 + πn, n ∈ Z;

x ∈ [–72; 72]; x ∈ [–72; 72];

x = ± 72;

x = 1 + 2n, n ∈ Z;

x ∈ [–72; 72]