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1)tg²x+ctg²x+3tgx+3cygx=-4
(tgx+ctgx)²-2tgxctgx+3(tgx+ctgx)+4=0 tgx*ctgx=1
(tgx+ctgx)²+3(tgx+ctgx)+2=0
tgx+ctgx=a
a²+3a+2=0
a1+a2=-3 U a1*a2=2
a1=-2⇒tgx+ctgx=-2
tgx+1/tgx+2=0
tg²x+2tgx+1=0 tgx≠0
(tgx+1)²=0⇒tgx=-1⇒x=-π/4+πn
a2=-1⇒tgx+ctgx=-1
tgx+1/tgx+1=0
tg²x+tgx+1=0 tgx≠0
tgx=t⇒t²+t+1=0
D=1-4=-3-решения нет
2)(1-сos2x)/2+(1-cos4x)/2=(1+cos6x)/2+(1+cos8x)/2
1-cos2x+1-cos4x=1+cos6x+1+cos8x
cos8x+cos6x+cos4x+cos2x=0
2cos5xcos3x+2cos5xcosx=0
2cos5x(cos3x+cosx)=0
2cos5x*2cos2xcosx=0
4cos5xcos2xcosx=0
cos5x=0⇒5x=π/2+πn⇒x=π/10+πn/5
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
cosx=0⇒x=π/2+πn
А) 2x^2-7x-9<0
Решаю по дискриминанту
D=49-4*2*(-9)
D=121
x=-b+-корень из D/2a
x=7+-11/4
x1=7+11/4=18/4=4,5
x2=7-11/4=-4/4=-1
б)x^2>49
x>7 или -7
5x² + 3x - 8 = 0
D = b² - 4ac = 9 - 4 × 5 × (-8) = 9 + 160 = 169 = 13²
x1 = ( - 3 + 13) / 10 = 1
x2 = ( - 3 - 13) / 10 = - 1,6
Ответ: x1 = 1, x2 = - 1,6.
(2x + 3)( 3x + 1) = 11x + 30
6x² + 11x + 3 = 11x + 30
6x² + 11x - 11x = 30 - 3
6x² = 27
6x² - 27 = 0
2x² - 9 = 0
2x² = 9
x² = 4,5
x1,2 = +/-√4,5
Ответ: x1,2 = +/-√4,5
x² + 4x - 2 = 0
D = b² - 4ac = 16 - 4 × (-2) = 16 + 8 = 24
x1 = ( - 4 + 2√6) / 2 =-2(2-√6)/2 = - (2 - √6) = - 2 + √6
x2 = ( - 4 - 2√6) / 2 =-2(2 + √6)/2 = -(2 + √6) = - 2 - √6
Ответ: x1 = - 2 + √6, x2 = - 2 - √6.