arcsin(-1/√2)-arcsin1+arcsin(√3/2)= -arcsin(1/√2)-π/2+π/3= -π/4-π/2+π/3=
=(-3π-6π+4π)/12= -5π/12
Упростить выражение
1. думаю не (x-2) -(x+2)³ а (x-2)³ -(x+2)³ .
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(x-2)³-(x+2)³ =( x-2-(x+2) ) ( (x-2)² +(x-2)(x+2) +(x+2)² ) =
- 4(x² -4x+4 +x² -4 +x² +4x+4) = - 4(3x² +4).
-------- или a³+b³ = (a-b)³ +3ab(a-b)--------
(х-2)³-(х+2)³ =(х-2-(х+2) )³ +3(х-2)*(х+2)* (х-2- (х+2) ) =
(-4)³ +3(x² -4)*(-4) = -4((-4)² +3(x² -4) ) = -4(3x²+4).
2.
(a⁶ - 3a³ +9)(a³+3) - a⁹ =(a³+3)( (a³)² - a³*3 +3²) - a⁹ =(a³)³+3³ -a⁹=
a⁹+ 27 -a⁹= 27.
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3.
(a+3)³-(a-1)³-12a² =a³ +3a²*3+3a*3²+3³ -(a³ -3a²+3a -1) -12a² =
a³ +9a²+27a+27 -a³ +3a²-3a +1 -12a² =24a+28 =4(6a+7).
---- или
(a+3)³-(a-1)³-12a² =(a+3-(a-1) )( (a+3)² +(a+3)(a-1) +(a-1)² ) -12a² =
4( a²+6a+9 +a²+2a-3 +a²-2a+1 ) -12a² =4(3a²+6a+7 ) -12a² =
=12a²+4(6a+7) -12a² =4(6a+7).
Просто замени a на 2 и сократи 3 и 3 в последнем действии.
![\frac{3{a}^{2} }{2a - 1} = \frac{3 \times {2}^{2} }{2 \times 2 - 1} = \frac{3 \times 4}{3} = 4](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7Ba%7D%5E%7B2%7D+%7D%7B2a+-+1%7D+%3D++%5Cfrac%7B3+%5Ctimes++%7B2%7D%5E%7B2%7D+%7D%7B2+%5Ctimes+2+-+1%7D+%3D+%5Cfrac%7B3+%5Ctimes+4%7D%7B3%7D++%3D+4)