(x^2-1)(x^2+5x+6)=60
giúp mình hic
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\(40+2\left(12-x\right)=60\)
\(2\left(12-x\right)=20\)
\(12-x=10\)
\(x=2\)
\(\left(5x+2\right)\left(x-1\right)-3\left(x+3\right)^2-2\left(x-6\right)\left(x+6\right)\)
\(=5x^2-5x+2x-2-3\left(x^2+6x+9\right)-2\left(x^2-6^2\right)\)
\(=5x^2-3x-2-3x^2-18x-27-2x^2+72\)
\(=-21x+43\)
Ta có: \(\left(x^2-1\right)\left(x^2+5x+6\right)=60\)
=>\(x^4+5x^3+6x^2-x^2-5x-6-60=0\)
=>\(x^4+5x^3+5x^2-5x-66=0\)
=>\(x^4-2x^3+7x^3-14x^2+19x^2-38x+33x-66=0\)
=>(x-2)(\(x^3+7x^2+19x+33)\) =0
TH1: x-2=0
=>x=2
TH2: \(x^3+7x^2+19x+33=0\)
=>x≃-4,38
\(\lim\limits_{x\rightarrow-\infty}\dfrac{x-5x^2+1}{x^2-1}=\lim\limits_{x\rightarrow-\infty}\dfrac{\dfrac{1}{x}-5+\dfrac{1}{x^2}}{1-\dfrac{1}{x^2}}=\dfrac{-5}{1}=-5\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{5x^3\left(2-x^2\right)^3\left(4x^2+1\right)^2}{4x^{13}+x^2-6}=\lim\limits_{x\rightarrow+\infty}\dfrac{5\left(\dfrac{2}{x^2}-1\right)^3\left(4+\dfrac{1}{x^2}\right)^2}{4+\dfrac{1}{x^{11}}-\dfrac{6}{x^{13}}}=\dfrac{5.\left(-1\right)^3.4^2}{4}=-20\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{4x-\sqrt{9x^2+x}}{3-x}=\lim\limits_{x\rightarrow+\infty}\dfrac{4-\sqrt{9+\dfrac{1}{x}}}{\dfrac{3}{x}-1}=\dfrac{4-3}{-1}=-1\)