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b) 37,5 . 6,5 – 7,5 . 3,4 – 6,6 . 7,5 + 3,5 . 37,5 = (37,5 . 6,5 + 3,5 . 37,5) - (7,5 . 3,4 + 6,6 . 7,5) = 37,5(6,5 + 3,5) - 7,5(3,4 + 6,6) = 37,5 . 10 - 7,5 . 10 = 375 - 75 = 300.
a) 45^2 + 40^2 – 15^2 + 80 . 45 = 45^2 +2 . 40 . 45 + 40^2 – 15^2 = (40 + 45)^2 – 15^2 = 852 – 152 = (85 – 15)(85 + 15) = 70 . 100 = 7000.
a) \(x\left(2x-1\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=3,5\)
\(\Leftrightarrow2x^3-x^2+10x^2-5x-2x^3-x-9x^2-4,5=3,5\)
\(\Leftrightarrow-6x=8\Leftrightarrow x=-\frac{4}{3}\)
b) \(\left(2x-5\right)^2+\left(y-3\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}2x-5=0\\y-3=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{5}{2}\\y=3\end{cases}}}\)
a) x\left(2x-1\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=3,5x(2x−1)(x+5)−(2x2+1)(x+4,5)=3,5
\Leftrightarrow2x^3-x^2+10x^2-5x-2x^3-x-9x^2-4,5=3,5⇔2x3−x2+10x2−5x−2x3−x−9x2−4,5=3,5
\Leftrightarrow-6x=8\Leftrightarrow x=-\frac{4}{3}⇔−6x=8⇔x=−34
b) \left(2x-5\right)^2+\left(y-3\right)^2=0(2x−5)2+(y−3)2=0
\(\Leftrightarrow\hept{\begin{cases}2x-5=0\\y-3=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{5}{2}\\y=3\end{cases}}}\)
\(a,3x+2\left(5-x\right)=0\)
\(\Rightarrow3x+10-2x=0\)
\(\Rightarrow x+10=0\)
\(\Rightarrow x=-10\)
\(b,x\left(2x-1\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=3,5\)
\(\Rightarrow\left(2x^2-x\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=3,5\)
\(\Rightarrow2x^3+9x^2-5x-2x^3-9x^2-4,5=3,5\)
\(\Rightarrow-5x-4,5=3,5\)
\(\Rightarrow-5x=8\)
\(\Rightarrow x=-\dfrac{8}{5}\)
\(c,3x^2-3x\left(x-2\right)=36\)
\(\Rightarrow3x^2-3x^2+6x=36\)
\(\Rightarrow6x=36\)
\(\Rightarrow x=6\)
\(d,\left(3x^2-x+1\right)\left(x-1\right)=x^2\left(4-3x\right)=\dfrac{5}{2}\)
\(\Rightarrow3x^3-3x^2-x^2+x+x-1+4x^2-3x^3=\dfrac{5}{2}\)
\(\Rightarrow2x-1=\dfrac{5}{2}\)
\(\Rightarrow2x=\dfrac{7}{2}\)
\(\Rightarrow x=\dfrac{7}{4}\)
a)\(37,5\times8,5+-7,5\times3,4-6,6\times7,5+1,5\times37,5\)
\(=\left(37,5\times8,5+1,5\times37,5\right)-\left(7,5\times3,4+6,6\times7,5\right)\)
\(=37,5\left(8,5+1,5\right)-7,5\left(3,4+6,6\right)\)
\(=375-75\)
\(=300\)
a2 + b2 + c2 + 3,5 = a + 2b + 3c
<=> (a2 - a + 0,25) + (b2 - 2b + 1) + (c2 - 3c + 2,25) = 0
<=> (a - 0,5)2 + (b - 1)2 + (c - 1,5)2 = 0
<=> (a; b; c) = (0,5; 1; 1,5)
a)43,5.5,5-3,5.2,7+43,5.4,5-3,5.7.3
=(43,5.5,5+43,5.4,5)+(-3,5.2,7-3,5.7,3)
=43,5.(5,5+4,5)-3,5.(2,7+7,3)
=43,5.10-3,5.10
=435-35
=400
b)352+402-252+40.70
=(352-252)+402+40.70
=(35-25).(35+25)+402+40.70
=10.60+402+40.70
=600+1600+2800
=2200+2800
=5000