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M=(x2+6x+9)-10
=(x+3)2-10≥-10
Dấu = khi x+3=0 khi x=-3
Vậy GTNN của M =-10 khi x=-3
\(A=1\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)
\(=...\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)
\(=2^{64}-1-2^{64}=-1\)
\(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\\ 4x^2-4x+1+x^2+6x+9-5x^2+245=0\\ 2x+255=0\\ 2x=-255\\ x=-\dfrac{255}{2}\)
Ta có : 4x2 - 25 - (2x - 5)(2x + 7) = 0
<=> (2x)2 - 52 - (2x - 5)(2x + 7) = 0
=> (2x - 5)(2x + 5) - (2x - 5)(2x + 7) = 0
=> (2x - 5)(2x + 5 - 2x - 7) = 0
=> (2x - 5)(-2) = 0
=> 2x - 5 = 0
=> 2x = 5
=> x = 5/2
b) ta có: x^3 +27+(x+3)(x-9)=0
<=>x^3 +27 +x^2 -6x-27=0
<=>x^3 +x^2-6x=0
<=>(x^3 -2x^2) +(3.x^2 -6x)=0
<=>x^2(x-2)+3x(x-2)=0
<=>(x^2 +3x)(x-2)=0
<=>x(x+3)(x-2)=0=> x=0 hoặc x+3=0 hoặc x-2=0=>x=0 hoặc x=-3 hoặc x=2
\(\left(-3x-2\right)^2+\left(3x+5\right)\left(5-3x\right)=-7\)
\(\Leftrightarrow9x^2+12x+4+15x-9x^2+25-15x=-7\)
\(\Leftrightarrow12x+36=0\Leftrightarrow x=-3\)
\(\left(x+2\right)\left(x^2+2x+2\right)-x\left(x-8\right)^2=\left(4x-3\right)\left(4x+3\right)\)
\(\Leftrightarrow x^3+2x^2+2x+2x^2+4x+4-x\left(x^2-16x+64\right)=16x^2-9\)
\(\Leftrightarrow x^3+4x^2+6x+4-x^3+16x^2-64=16x^2-9\)
\(\Leftrightarrow4x^2+6x-51=0\)
\(\cdot\Delta=6^2-4.4.\left(-51\right)=852\)
Vậy pt có 2 nghiệm phân biệt
\(x_1=\frac{-6+\sqrt{852}}{8}\);\(x_2=\frac{-6-\sqrt{852}}{8}\)
Ta có: \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)
\(\Leftrightarrow4x^2-14x+10x-35-\left[-\left(4x+3\right)\right]^2=16\)
\(\Leftrightarrow4x^2-4x-35-\left(-1\right)^2\cdot\left(4x+3\right)^2-16=0\)
\(\Leftrightarrow4x^2-4x-35-\left(4x+3\right)^2-16=0\)
\(\Leftrightarrow4x^2-4x-35-\left(16x^2+24x+9\right)-16=0\)
\(\Leftrightarrow4x^2-4x-35-16x^2-24x-9-16=0\)
\(\Leftrightarrow-12x^2-28x-60=0\)
\(\Leftrightarrow-12\left(x^2+\frac{28}{12}x+5\right)=0\)
\(\Leftrightarrow x^2+\frac{28}{12}x+5=0\)
\(\Leftrightarrow x^2+2\cdot x\cdot\frac{7}{6}+\frac{49}{36}+\frac{131}{36}=0\)
\(\Leftrightarrow\left(x+\frac{7}{6}\right)^2+\frac{131}{36}=0\)(vô lý)
Vậy: \(S=\varnothing\)