Решение задания приложено
Способ сложения:
{ 4x + 7y = 90 | × 3
{-6x + 5y = 20 | × 2
{ 12x + 21y = 270
{-12x + 10y = 40
12х + 21у + ( - 12х + 10у) = 270 + 40
31у = 310
у = 310÷31
у = 10
4х + 7×10 = 90
4х + 70 = 90
4х = 90 - 70
4х = 20
х = 20 ÷ 4
х = 5
Способ подстановки :
{4x + 7y = 90
{-6x + 5y = 20 ⇒ 5y = 20 +6x ⇒ y = 2(10+3x)/5 ⇒ y =0,4(10+3x)
4x + 7× 0,4(10+3x) = 90
4x + 2,8(10+3x) = 90
4x + 28 + 8,4x = 90
12,4x = 90 - 28
12,4x = 62
х = 62 ÷ 12,4
х = 5
y = 0,4×(10 + 3×5) = 0,4 × 25
у = 10
ответ : ( 5 ; 10) .
А)
4cos a/2*cos b/2*cos y/2 = sin a + sin b + sin y
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4cos α/2*cos β/2*cosγ/2 =
2(cos(α+β)/2 +cos(α-β)/2)*cosγ/2 =
2cos(α+β)/2*cosγ/2 +2cosγ/2 *cos(α-β)/2=
cos(α+β+γ)/2 +cos(α+β-γ)<span>/2+</span>cos(α+γ-β)/2 +cos(γ+β-α)<span>/2 =
</span>cosπ/2 +cos(α+β+γ -2γ)/2+cos(α+β+γ-2β)/2 +cos(β+γ+α-2α)/2=
cos(π -2γ)/2+cos(π-2β)/2 +cos(π-α)/2=
cos(π/2 -γ)+cos(π/2-β) +cos(π/2-α) = sinα +sinβ+sinγ.
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б) 4sin(α/2)*sin(β/2)*cos(γ/2) = sin α + sin <span>β</span> - sin γ
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sin α + sin β - sinγ =2sin((α+c)/2)*cos((α-β)/2) -sin(π-(α+<span>β))=
</span>2sin((α+β)/2)*cos((α-β)/2) -sin(α+<span>β)=
</span>2sin((α+β)/2)*cos((α-β)/2) -sin2*((α+<span>β)/2)=
</span>2sin((α+β)/2)*cos((α-β)/2) -2sin((α+β)/2)*cos((α<span>+β)/2) =
</span>2sin((α+β)/2)*(cos((α-β)/2) -cos((α<span>+β)/2) )=
</span>2sin((π-γ)/2) *(-2sin(α/2)*sin(-β/2) =2sin(π/2-γ/2) *2sin(α/2)*sin(β/2)=
2cos(γ/2) *2sin(α/2)*sin(β/2) =4sin(α/2)*sin(β/2)*cos(γ/2) .
вынесем Х квадрат: х^2(х^2-10х+9)=0