Б)найдите все корни этого уравнения, принадлежащие промежутку ( ; )

√2cos^2x+sin(π/2-x)=0 √2cos^2x+cosx=0 cosx(√2cosx+1)=0 cosx=0,x=π/2+πn cosx=-1/√2,x =+-3/4π+2πn -3/2π; -5/4π; =3/4π; -π/2; π/2; 3/4π

A4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 (a-b)•(b-c)•(c-a)

reformatting the input :

changes made to your input should not affect the solution:   (1): "c2"     was replaced by    "c^2".    2 more similar replacement(s).

step by step solution : skip ad step    1    : c2 simplify c - a equation at the end of step    1    : (a2) (b2) c2 •(a-c))+•(b-+•(c-b)) (a-b) (b-c) c-a step    2    : equation at the end of step    2    : (a2) (b2) c2•(c-b) •(a-c))+•(b-+ (a-b) (b-c) c-a step   3  : b2 simplify b - c equation at the end of step    3    : (a2) b2 c2•(c-b) •(a-c))+•(b-+ (a-b) b-c c-a step    4    : equation at the end of step    4    : (a2) b2•(b-a) c2•(c-b) •(a-c))++ (a-b) b-c c-a step   5  : a2 simplify a - b equation at the end of step    5    : a2 b2•(b-a) c2•(c-b) •(a-c))++ a-b b-c c-a step    6    : equation at the end of step    6    : a2•(a-c) b2•(b-a) c2•(c-b) ++ a-b b-c c-a step    7    : calculating the least common multiple :

  7.1      find the least common multiple            the left  denominator  is :             a-b            the right  denominator  is :             b-c 

                                    number of times each algebraic factor                        appears in the factorization of:         algebraic                factor          left    denominator    right    denominator    l.c.m = max    {left,right}    a-b  101  b-c  011

          least common multiple:               (a-b)  •  (b-c) 

calculating multipliers :

  7.2      calculate multipliers for the two fractions        denote the least common multiple by    l.c.m        denote the left multiplier by    left_m        denote the right multiplier by    right_m        denote the left deniminator by    l_deno        denote the right multiplier by    r_deno        left_m  =  l.c.m  /  l_deno  =  b-c      right_m  =  l.c.m  /  r_deno  =  a-b

making equivalent fractions :

  7.3          rewrite the two fractions into  equivalent fractionstwo fractions are called  equivalent  if they have the  same numeric value.for example :   1/2     and    2/4    are equivalent,    y/(y+1)2      and    (y2+y)/(y+1)3    are equivalent as well.  to calculate  equivalent fraction  , multiply the  numerator  of each fraction, by its respective  multiplier.

l. mult. • l. num. a2 • (a-c) • (b-c) = l.c.m (a-b) • (b-c) r. mult. • r. num. b2 • (b-a) • (a-b) = l.c.m (a-b) • (b-c) adding fractions that have a common denominator :

  7.4            adding up the two equivalent fractions  add the two equivalent fractions which now have a common denominatorcombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 = (a-b) • (b-c) (a - b) • (b - c) equation at the end of step    7    : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) + (a - b) • (b - c) c - a step    8    : calculating the least common multiple :

  8.1      find the least common multiple            the left  denominator  is :             (a-b)  •  (b-c)            the right  denominator  is :             c-a 

                                    number of times each algebraic factor                        appears in the factorization of:         algebraic                factor          left    denominator    right    denominator    l.c.m = max    {left,right}    a-b  101  b-c  101  c-a  011

          least common multiple:               (a-b)  •  (b-c)  •  (c-a) 

calculating multipliers :

  8.2      calculate multipliers for the two fractions        denote the least common multiple by    l.c.m        denote the left multiplier by    left_m        denote the right multiplier by    right_m        denote the left deniminator by    l_deno        denote the right multiplier by    r_deno        left_m  =  l.c.m  /  l_deno  =  c-a      right_m  =  l.c.m  /  r_deno  =  (a-b)•(b-c)

making equivalent fractions :

  8.3          rewrite the two fractions into  equivalent fractions

l. mult. • l. num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) = l.c.m (a-b) • (b-c) • (c-a) r. mult. • r. num. c2 • (c-b) • (a-b) • (b-c) = l.c.m (a-b) • (b-c) • (c-a) adding fractions that have a common denominator :

  8.4            adding up the two equivalent fractions 

(a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) + c2 • (c-b) • (a-b) • (b-c) -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 = (a-b) • (b-c) • (c-a) (a-b) • (b-c) • (c-a) final result : -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 (a-b)•(b-c)•(c-a)

processing ends successfully

latest drills solved (-4,7)to(94,-55)(5)/(7)+(4)/(y)=38(x+8/9)-9 a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b) 

4ч 48 мин=240+48=288 мин применим формулу суммы первых n-членов арифметической прогрессии. дано: a1=22           d=4           s(n)=288 найти: n=? s(n)=(2a₁+d(n-1))/2*n 288=(2*22+4(n-1))/2*n (44+4n-4)/2*n=288 (40+4n)/2*n=288 40n+4n²=576    одз: n> 0 (количество может измеряться только n²+10n-144=0                      в положительных значениях)  d=100+576=676    √676=26 n₁=(-10+26)/2=8 n₂=(-10-26)/2=-18 - лишний корень, не входит в   одз    ответ: 8 дней. проверка: s₈=(2*22+4*7)/2*8=72/2*8=36*8=288