1)3000+400+50+6
2)40
3)200000+30000+400+50
4)4000000+5000+200
{2x-3y=4
{x+2y=-5/*(-2)⇒-2x-4y=10
прибавим
-7y=14
y=14:(-7)
y=-2
x+2*(-2)=-5
x=-5+4
x=-1
Ответ (-1;-2)
<span>(b-7)^2-9b^2=(b-7-3b)(b-7+3b)=(-2b-7)(4b-7)=-(2b+7)(4b-7)</span>
Решить <span> уравнения 4 * 16^sin^2x - 6 * 4^cos2x = 29
и найт</span>и все корни уравнения, принадлежащие отрезку [3π/2; 3π<span>] </span>
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4* (4² ^sin²x) -6*4^cos2x = 29⇔ 4* 4 ^(2sin²x) -6*4^cos2x = 29 ⇔
4* 4 ^ (1 -cos2x) -6*4^cos2x = 29 ⇔4* 4¹*4^( -cos2x) - 6*4^cos2x = 29 ⇔
4* 4 * 1 / ( 4^cos2x) - 6*4^cos2x = 29 ; * * * можно замена :t =4^cos2x * * *<span>
6* (4^ cos</span>2x)² +29* (4^ cos2x) -16 =0 ;
* * * (4^ cos2x)² +(29/6)* (4^ cos<span>2x)-8/3=0 * * * </span>
a) 4^cos<span>2x = -16 /3 < 0 не имеет решения </span><span> ; </span><span>
b) 4^cos</span>2x = 1/2 ⇔2 ^(2cos2x) = 2⁻¹ ⇔2cos2x = -1 ⇔ <span>cos2x = -1/2 .
</span>⇔2x = ±π/3 +2πn ,n ∈Z ;
x = ±π/6 +πn ,n ∈Z .
* * * * * * *
Выделяем все корни уравнения, принадлежащие отрезку [3π/2; 3π] .<span>
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3</span>π/2 ≤ - π/6 +πn ≤ 3π ⇔ 3π/2+π/6 ≤ πn ≤ 3π+π/6 ⇔ 5/3 ≤ n ≤ 19/6⇒
n =2 ; 3 .
x₁= - π/6 +2π =11π/6 ; x₂ = - π/6 +3π =1<span>7π/</span>6 .
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3π/2 ≤ π/6 +πn ≤ 3π ⇔3π/2 -π/6 ≤ πn ≤ 3π -π/6 ⇔4/3 ≤ n ≤ 17/6⇒
n=2
x ₃ = π/6 +2π=13<span>π /6 .
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