X^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 0
Найдем значения многочлена в целых точках:
y(0) = 1 > 0
y(1) = 1 + 24 - 10 + 21 - 65 + 1 = 47 - 75 = -28 < 0
x1 ∈ (0; 1)
y(2) = 32 + 24*16 - 10*8 + 21*4 - 65*2 + 1 = 291 > 0
x2 ∈ (1; 2)
y(-1) = -1 + 24 + 10 + 21 + 65 + 1 = 120 > 0
y(-2) = -32 + 24*16 + 10*8 + 21*4 + 65*2 + 1 = 647 > 0
...
y(-24) = -7962624+24*331776+138240+21*576+65*24+1 = 151897 > 0
y(-25) = -9765625+24*390625+156250+21*625+65*25+1=-219624 < 0
x3 ∈ (-25; -24)
Дальше надо уточнять.
y(0,1) = 0,00001+24*0,0001-10*0,001+21*0,01-65*0,1+1 = -5,29759 < 0
y(0,02)=(0,02)^5+24(0,02)^4-10(0,02)^3+21(0,02)^2-65*0,02+1 = -0,29 < 0
y(0,01)=(0,01)^5+24(0,01)^4-10(0,01)^3+21(0,01)^2-65*0,01+1 = 0,352 > 0
x1 ∈ (0,01; 0,02)
y(0,015) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 0,03 ≈ 0
x1 ≈ 0,015
y(1,3) = (1,3)^5 + 24(1,3)^4 - 10(1,3)^3 + 21(1,3)^2 - 65*1,3 + 1 = 2,28 > 0
y(1,28) = (1,28)^5+24(1,28)^4-10(1,28)^3+21(1,28)^2-65*1,28 + 1 = -0,9 < 0
y(1,29) = (1,29)^5+24(1,29)^4-10(1,29)^3+21(1,29)^2-65*1,29 + 1 = 0,663 > 0
x2 ∈ (1,28; 1,29)
y(1,286) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 0,03 ≈ 0
x2 ≈ 1,286
y(-24,5) = -24,5^5+24*24,5^4+10*24,5^3+21*24,5^2+65*24,5+1 = -18890 < 0
y(-24,4) = -24,4^5+24*24,4^4+10*24,4^3+21*24,4^2+65*24,4+1 = 17576 > 0
y(-24,45) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = -509 < 0
y(-24,448) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 220 > 0
y(-24,449) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = -144 < 0
x ∈ (-24,448; -24,449)
Но числа еще достаточно далеко от 0, нужно уточнять дальше.
y(-24,4486) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 1,686 > 0
y(-24,44861) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = -1,959 < 0
y(-24,448605) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = -0,13 < 0
y(-24,448604) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 0,23 > 0
y(-24,4486045) = x^5 + 24x^4 - 10x^3 + 21x^2 - 65x + 1 = 0,046 ≈ 0
x ≈ -24,4486045
Ответ:
Объяснение:
121.
(a/3+b/6)* 1/2a+b)= (6a+3b)/18 * 1/(2a+b)=3(2a+b)/18 *1/(2a+b)=3/18=1/6
123.
(x/y-y/x)*2xy/(x-y)=(x²-y²)/xy * 2xy/(x-y)=(x-y)(x+y) *2/(x-y)=2(x+y)
125.
(5+a/b) *b/(5b+a)²=(5b+a)/b*b/(5b+a)²= 1/(5b+a)
127.
(a-3)/(a+3) *[ (a+a²/(3-a)]=(a-3)/(a+3) *[a(3-a)+a²]/(3-a)= =-(3-a)(a+3)* (3a-a²+a²)/(3-a)=
= -3a/(a+3)
129.
(x+5)/(x³+25x) * [(x+5)/(x-5) +(x-5)/(x+5)=(x+5)/x(x²+25) *[(x+5)²+(x-5)²]/(x²-25)=
=(x+5)/x(x²+25) *[(x²+10x+25+x²-10x+25)/(x-5)(x+5)]=(x+5)/x(x²+25) *(2x²+50)/(x-5)(x+5)=1/x(x²+25) *2(x²+25)/(x-5)= 1/x(x-5)