Cách Chứng minh phương trình vô số nghiệm

a)\(x^{4}+2x^{3}+5x^{2}+4x-12=0\);

b) \(x^{4}+2x^{3}-4x^{2}-5x-6=0\);

c)\(\left ( 3-x \right )^{4}+\left ( 2-x \right )^{4}=\left ( 5-2x \right )^{4}\);

d) \(\left ( x-4,5 \right )^{4}+\left ( x-5,5 \right )^{4}=1\).

a)\(x^{4}-4x^{3}-19x^{2}+106x-120=0\);

b)\(4x^{4}+12x^{3}+5x^{2}-6x-15=0\);

c)\(\left ( x+1 \right )\left ( x+2 \right )\left ( x+4 \right )\left ( x+5 \right )=40\).

a)\(3x^{3}+2x^{2}+2x+3=0\);

b)\(\left ( x^{2} +x+1\right )^{2}+\left ( x^{2} +x+1\right )-12=0\);

c)\(\left ( x^{2} +5x\right )^{2}-2x^{2}-10x=24\);

d)\(\left ( x^{2} +3x-4\right )^{3}+\left ( 2x^{2} -5x+3\right )^{3}\)\(=\left ( 3x^{2} -2x-1\right )^{3}\);

e)\(\left ( x-6 \right )^{4}+\left ( x-8 \right )^{4}=16\)

\(x^{3}-7x^{2}+15x-25=0\)

a)\(\left ( x+1 \right )^{3}+\left ( x-2 \right )^{3}=\left ( 2x-1 \right )^{3}\);

b)\(x^{3}+\left ( x+1 \right )^{3}+\left ( x+2 \right )^{3}=\left ( x+3 \right )^{3}\);

c)\(\left ( x+1 \right )^{4}+\left ( x+3 \right )^{4}=82\).

\(\left ( 2x^{2} +3x-1\right )^{2}-5\left ( 2x^{2}+3x+3 \right )+24=0\)

a) \(x\left ( x+3 \right )+a\left ( a-3 \right )=2\left ( ax-1 \right )\);

b)\(x^{2}+7x-a^{2}+a+12=0\).

a) \(x ^ {3} + x ^ {2} + x + 1 = 0 \);

b) \(x ^ {3} + x ^ {2}-x-1 = 0 \);

c) \(\left (x + 1 \right) ^ {2} \left (x + 2 \right) + \left (x + 1 \right) ^ {2} \left (x-2 \right) = -24 \);

d) \(2x ^ {3} + 3x ^ {2} + 6x + 5 = 0 \).