Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(5x^2+0=0\)
- \(x^2-49=0\)
- \(-5(-8x^2-3)=-(-43x^2-207)\)
- \(2(6x^2-8)=-(-14x^2+258)\)
- \(-6x^2+6=0\)
- \(-2(7x^2-5)=-(16x^2-12)\)
- \(x^2+91=7x^2-5\)
- \(-5(-3x^2-5)=-(-23x^2-673)\)
- \(-7x^2-334=-9x^2+4\)
- \(-2x^2-4=5x^2-4\)
- \(6x^2+384=0\)
- \(-8x^2+1800=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(5x^2+0=0 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(x^2-49=0 \\
\Leftrightarrow x^2 = 49 \\
\Leftrightarrow x^2 = \frac{49}{1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-5(-8x^2-3)=-(-43x^2-207) \\ \Leftrightarrow 40x^2+15=43x^2+207 \\
\Leftrightarrow 40x^2-43x^2=207-15 \\
\Leftrightarrow -3x^2 = 192 \\
\Leftrightarrow x^2 = \frac{192}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(6x^2-8)=-(-14x^2+258) \\ \Leftrightarrow 12x^2-16=14x^2-258 \\
\Leftrightarrow 12x^2-14x^2=-258+16 \\
\Leftrightarrow -2x^2 = -242 \\
\Leftrightarrow x^2 = \frac{-242}{-2}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-6x^2+6=0 \\
\Leftrightarrow -6x^2 = -6 \\
\Leftrightarrow x^2 = \frac{-6}{-6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-2(7x^2-5)=-(16x^2-12) \\ \Leftrightarrow -14x^2+10=-16x^2+12 \\
\Leftrightarrow -14x^2+16x^2=12-10 \\
\Leftrightarrow 2x^2 = 2 \\
\Leftrightarrow x^2 = \frac{2}{2}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(x^2+91=7x^2-5 \\ \Leftrightarrow x^2-7x^2=-5-91 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5(-3x^2-5)=-(-23x^2-673) \\ \Leftrightarrow 15x^2+25=23x^2+673 \\
\Leftrightarrow 15x^2-23x^2=673-25 \\
\Leftrightarrow -8x^2 = 648 \\
\Leftrightarrow x^2 = \frac{648}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-334=-9x^2+4 \\ \Leftrightarrow -7x^2+9x^2=4+334 \\
\Leftrightarrow 2x^2 = 338 \\
\Leftrightarrow x^2 = \frac{338}{2}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-2x^2-4=5x^2-4 \\ \Leftrightarrow -2x^2-5x^2=-4+4 \\
\Leftrightarrow -7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(6x^2+384=0 \\
\Leftrightarrow 6x^2 = -384 \\
\Leftrightarrow x^2 = \frac{-384}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+1800=0 \\
\Leftrightarrow -8x^2 = -1800 \\
\Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)