Cos(π/4-t)=cos(π/2-(π/4+t))=sin(π/4+t)
cos(5π/12+t)=cos(π/2-(π/12-t))=sin(π/12-t)
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cos(π/4+t)cos(π/12-t)-sin(π/4+t)sin(π/12-t)=cos(π/4+t+π/12-t)=
=cosπ/3=1/2
9a² + 6a+1 = (3a)² + 2 * 3a * 1 + 1² = (3a + 1)²
4^(x-3) - 71*2^(x-6) + 7 ≤ 0
2^(2x-6) - 71*2^(x-6) + 7 ≤ 0
(1/64)*2^(2x) - (71/64)*2^(x) + 7 ≤ 0
Замена: 2^(x) = t > 0
(1/64)*t^2 - (71/64)*t + 7 ≤ 0
t^2 - 71t + 448 ≤ 0
D = 3249 = 57^2
t1 = (71-57)/2 = 7 > 0
t2 = (71+57)/2 = 64 > 0
7 ≤ t ≤ 64
7 ≤ 2^x ≤ 64
log2(7) ≤ x ≤ 6