Tg(a+b)=(tga+tgb)/(1-tgatgb);tg(a-b)=(tga-tgb)/(1+tgatgb)
-----------------------------
tg(a+π/4)+tg(a-π/4)=(tga+tgπ/4)/(1-tgatgπ/4)+(tga-tgπ/4)/(1+tgatgπ/4)=
=(tga+1)/(1-tga)+(tga-1)/(1+tga)=[(tga+1)²-(tga-1)²]/[(1-tga)(1+tga)]=
=(1+2tga+tg²a-tg²a+2tga-1)/(1-tg²a)=4tga/(1-tg²a)=2tg2a
34.4
34.5
5a²+10ab +5b² = 5(a²+2ab+b²)= 5(a+b)²= 5(a+b)(a+b)
2x²+4x+2 = 2(x²+2x+1) = 2(x+1)²= 2(x+1)(x+1)
3m²+3n²-6mn = 3(m² +n² -2mn) = 3(m² -2mn+n²)=
=3(m-n)²=3(m-n)(m-n)
8n² - 16n + 8 = 8(n² - 2n +1) = 8(n-1)² = 8(n-1)(n-1)
34.6
-3x²+12x-12= -3(x² -4x +4) = -3(x² -2*x*2+2²) = -3(x-2)²=-3(x-2)(x-2)
-2a³+20a²b -50ab²= -2a(a² -10ab+ 25b²) = -2a(a²-2*a*5b +(5b)²)=
=-2a(a-5b)² = -2a(a-5b)(a-5b)
-5p²-10pq -5q²= -5(p²+10pq+q²) = -5(p+q)²= -5(p+q)(p+q)
-36z³-24z²-4z = -4z(9z² + 6z +1)= -4z( (3a)² +2*3a*1 +1²)=
= -4z(3a+1)² = -4z(3a+1)(3a+1)
(2x + 3)(4x - 3)(x - 10) ≥ 0
Нули: x = -1,5; 0,75; 10.
- -1,5|||||+||||||||||0,75 - 10||||||+|||||||||
--------------●-------------------●-------------------------<span>●</span>----------------> x
Ответ: x ∈ [-1,5; 0,75] U [10; +∞).
(5 + x)(x + 1)(3 - x) < 0
-(5 + x)(x + 1)(x - 3) < 0
(x - 3)(x + 1)(x + 5) > 0
Нули: x = -5; -1; 3.
- -5||||||||||||||+|||||||||||||||-1 - 3|||||+|||||||||||||
-------------0-------------------------0-------------------0-----------> x
Ответ: x ∈ (-5; -1) U (3; +∞).
<span>{ 5x-2y=7
{ 3x+y=2
{ 5x-2y=7
{ 6x+2y=4
11x=11
x=1
3*1+y=2
3+y=2
y=2-3
y=-1
Otvet: (x,y)=(1,-1)</span>
√ 28 - √ 63 + √ 112 = 2√ 7 - 3√7 + 4√7 = 3 √ 7
0,1√ 270 * √ 30 + √ 196 = 0,1√( 270*30 ) + 14 = 0,1√( 9*30*30) + 14 = 0,1*3*30 + 14 =
= 9 + 14 = 23