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a, 35x 34+35x 38 + 65x 75+ 65x 45=10437

b, 36x 28 + 36x 82 + 64x 69 + 64 x41=11000

c, 254x 399 - 145/ 254+ 399 x 253=202292,4291

a: Ta có: \(24=2^3\cdot3;36=2^2\cdot3^2;160=2^5\cdot5\)

=>ƯCLN(24;36;160)=2^2=4

24⋮x; 36⋮x; 160⋮x

Do đó: x∈ƯC(24;36;160)

mà x lớn nhất

nên x=ƯCLN(24;36;160)=4

b: \(54=2\cdot3^3;12=2^2\cdot3\)

=>ƯCLN(54;12)=2*3=6

x∈ƯC(54;12)

mà x lớn nhất

nên x=ƯCLN(54;12)

=>x=6

c: \(4=2^2;6=2\cdot3\)

=>BCNN(4;6)=\(2^2\cdot3=12\)

x⋮4; x⋮6

=>x∈BC(4;6)

=>x∈B(12)

mà 0<x<50

nên x∈{12;24;36;48}

d: \(12=2^2\cdot3;18=2\cdot3^2\)

=>BCNN(12;18)=\(2^2\cdot3^2=36\)

x⋮12; x⋮18

=>x∈BC(12;18)

=>x∈B(36)

mà x<250

nên x∈{36;72;108;144;180;216}

e: \(36=2^2\cdot3^2;24=2^3\cdot3\)

=>ƯCLN(36;24)=\(2^2\cdot3=12\)

x∈ƯC(36;24)

=>x∈Ư(12)

mà x<=20

nên x∈{1;2;3;4;6;12}

f: \(91=13\cdot7;26=2\cdot13\)

=>ƯCLN(91;26)=13

91⋮x; 26⋮x

=>x∈ƯC(91;26)

=>x∈Ư(13)

mà 10<x<30

nên x=13

g: 2=2; 3=3; 5=5; 7=7

=>BCNN(2;3;5;7)=\(2\cdot3\cdot5\cdot7=210\)

x⋮2; x⋮3; x⋮5; x⋮7

=>x∈BC(2;3;5;7)

mà x nhỏ nhất

nên x=BCNN(2;3;5;7)

=>x=210

h: \(6=2\cdot3;4=2^2\)

=>BCNN(6;4)=\(2^2\cdot3=12\)

x∈BC(6;4)

=>x∈B(12)

mà 16<=x<=50

nên x∈{24;36;48}

Lạnh xun loz

phải không mày >

haizz

\(6x^4+7x^3-36x^2-7x+6=0\)

\(\Leftrightarrow\left(6x^4-11x^3-3x^2+2x\right)+\left(18x^3-33x^2-9x+6\right)=0\)

\(\Leftrightarrow x\left(6x^3-11x^2-3x+2\right)+3\left(6x^3-11x^2-3x+2\right)=0\)

\(\Leftrightarrow\left(6x^3-11x^2-3x+2\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[\left(6x^3-14x+4x\right)+\left(3x^2-7x+2\right)\right]\left(x+3\right)=0\)

\(\Leftrightarrow\left[2x\left(3x^2-7x+2\right)+\left(3x^2-7x+2\right)\right]\left(x+3\right)=0\)

\(\Leftrightarrow\left(3x^2-7x+2\right)\left(2x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(3x^2-6x-x+2\right)\left(2x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[3x\left(x-2\right)-\left(x-2\right)\right]\left(2x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(3x-1\right)\left(2x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\3x-1=0\end{cases}}\)hoặc \(\orbr{\begin{cases}2x+1=0\\x+3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=\frac{1}{3}\end{cases}}\)hoặc\(\orbr{\begin{cases}x=\frac{-1}{2}\\x=-3\end{cases}}\)

Vậy tập hợp nghiệm \(S=\left\{2;-3;\frac{1}{3};\frac{-1}{2}\right\}\)

6x⁴+7x³-36x²-7x+6=0

<=> 6x⁴-2x³+9x³-3x²-33x²+11x-18x+6=0

<=> 2x³(3x-1)+3x²(3x-1)-11x(3x-1)-6(3x-1)=0

<=> (3x-1)(2x³+3x²-11x-6)=0

<=>(3x-1)(2x³-4x²+7x²-14x+3x-6)=0

<=>(3x-1)[2x²(x-2)+7x(x-2)+3(x-2)]=0

<=>(3x-1)(x-2)(2x²+7x+3)=0

<=>(3x-1)(x-2)(2x²+6x+x+3)=0

<=>(3x-1)(x-2)[2x(x+3)+(x+3)]=0

<=>(3x-1)(x-2)(x+3)(2x+1)=0

th1: 3x+1=0 <=> x=\(-\frac{1}{3}\)

th2: x-2=0 <=> x=2

th3: x+3=0 <=> x=-3

th4: 2x+1=0 <=> x=-\(\frac{1}{2}\)