ответ: 1) x = (a + b) / (a - b); a ≠ b; 2) x = 2 · (m - n); 3) x = a + 1;
4) x = (3 · (m - n)) / (m + n); m ≠ - n
Объяснение:
1) a²x - b²x = a² + 2ab + b²; x · (a - b) · (a + b) = (a + b)²; x = (a + b)² / (a - b) · (a + b)
x = (a + b) / (a - b); a ≠ b
2) 3mx + 3nx = 6m² - 6n²; 3 · x · (m + n) = 6 · (m + n) · (m - n);
x = (6 · (m + n) · (m - n)) / 3 · (m + n); x = 2 · (m - n)
3) ax + x = a² + 2a + 1; x · (a + 1) = (a + 1)²; x = (a + 1)² / (a + 1) = a + 1; x = a + 1
4) m²x + 2mnx + n²x = 3m² - 3n²; x · (m + n)² = 3 · (m + n) · (m - n);
x = (3 · (m + n) · (m - n)) / (m + n)²; x = (3 · (m - n)) / (m + n); m ≠ - n
(cosx+sinx)/(cosx-sinx)=ctgx
(cosx+sinx)/(cosx-sinx)=cosx/sinx
cosxsinx+sin^2x-cos^2x+sinxcosx=0
sin2x-cos2x=0
sin2x=cos2x
tg2x=1
x=П/8+Пk/2
ответ х=П/8+Пk/2
2sin^2x+√3*sin2x=1+2cosx
2sin^2x-sin^2x-cos^2x+√3*sin2x=2cosx
√3*sin2x-cos2x=2cosx
cosx+cos(П/3+2x)=0
cos(3x/2+П/6)=0 cos(П/6+x/2)=0
3x/2+П/6=П/2+Пk x/2+П/6=П/2+Пk
x=2П/9+2Пk/3 x=2П/3+2Пk