Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3(9x^2-8)=-(34x^2-24)\)
- \(4(-8x^2-2)=-(28x^2-392)\)
- \(5(7x^2-6)=-(-37x^2+422)\)
- \(5(-7x^2+3)=-(43x^2-303)\)
- \(-3x^2-432=0\)
- \(4(-3x^2-9)=-(17x^2-144)\)
- \(5(5x^2-2)=-(-29x^2-474)\)
- \(-4x^2-330=-8x^2-6\)
- \(-4x^2+484=0\)
- \(-6x^2+1014=0\)
- \(5(-10x^2+2)=-(55x^2-855)\)
- \(-x^2+100=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3(9x^2-8)=-(34x^2-24) \\ \Leftrightarrow -27x^2+24=-34x^2+24 \\
\Leftrightarrow -27x^2+34x^2=24-24 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(4(-8x^2-2)=-(28x^2-392) \\ \Leftrightarrow -32x^2-8=-28x^2+392 \\
\Leftrightarrow -32x^2+28x^2=392+8 \\
\Leftrightarrow -4x^2 = 400 \\
\Leftrightarrow x^2 = \frac{400}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(7x^2-6)=-(-37x^2+422) \\ \Leftrightarrow 35x^2-30=37x^2-422 \\
\Leftrightarrow 35x^2-37x^2=-422+30 \\
\Leftrightarrow -2x^2 = -392 \\
\Leftrightarrow x^2 = \frac{-392}{-2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(5(-7x^2+3)=-(43x^2-303) \\ \Leftrightarrow -35x^2+15=-43x^2+303 \\
\Leftrightarrow -35x^2+43x^2=303-15 \\
\Leftrightarrow 8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{8}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-3x^2-432=0 \\
\Leftrightarrow -3x^2 = 432 \\
\Leftrightarrow x^2 = \frac{432}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(-3x^2-9)=-(17x^2-144) \\ \Leftrightarrow -12x^2-36=-17x^2+144 \\
\Leftrightarrow -12x^2+17x^2=144+36 \\
\Leftrightarrow 5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{5}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(5(5x^2-2)=-(-29x^2-474) \\ \Leftrightarrow 25x^2-10=29x^2+474 \\
\Leftrightarrow 25x^2-29x^2=474+10 \\
\Leftrightarrow -4x^2 = 484 \\
\Leftrightarrow x^2 = \frac{484}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-330=-8x^2-6 \\ \Leftrightarrow -4x^2+8x^2=-6+330 \\
\Leftrightarrow 4x^2 = 324 \\
\Leftrightarrow x^2 = \frac{324}{4}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-4x^2+484=0 \\
\Leftrightarrow -4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{-4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-6x^2+1014=0 \\
\Leftrightarrow -6x^2 = -1014 \\
\Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(5(-10x^2+2)=-(55x^2-855) \\ \Leftrightarrow -50x^2+10=-55x^2+855 \\
\Leftrightarrow -50x^2+55x^2=855-10 \\
\Leftrightarrow 5x^2 = 845 \\
\Leftrightarrow x^2 = \frac{845}{5}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-x^2+100=0 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)