Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(14x^2-385=6x^2+7\)
- \(3x^2-27=0\)
- \(4x^2+64=0\)
- \(-3(-5x^2+10)=-(-13x^2-420)\)
- \(-5(5x^2+2)=-(24x^2+9)\)
- \(-3x^2-9=-4x^2-9\)
- \(4x^2-713=9x^2+7\)
- \(-2(7x^2-3)=-(20x^2-6)\)
- \(-4(8x^2-2)=-(39x^2-1583)\)
- \(-3x^2-1023=3x^2-9\)
- \(-8x^2-1152=0\)
- \(-5(-8x^2-10)=-(-47x^2-750)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(14x^2-385=6x^2+7 \\ \Leftrightarrow 14x^2-6x^2=7+385 \\
\Leftrightarrow 8x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{8}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(3x^2-27=0 \\
\Leftrightarrow 3x^2 = 27 \\
\Leftrightarrow x^2 = \frac{27}{3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(4x^2+64=0 \\
\Leftrightarrow 4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(-5x^2+10)=-(-13x^2-420) \\ \Leftrightarrow 15x^2-30=13x^2+420 \\
\Leftrightarrow 15x^2-13x^2=420+30 \\
\Leftrightarrow 2x^2 = 450 \\
\Leftrightarrow x^2 = \frac{450}{2}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-5(5x^2+2)=-(24x^2+9) \\ \Leftrightarrow -25x^2-10=-24x^2-9 \\
\Leftrightarrow -25x^2+24x^2=-9+10 \\
\Leftrightarrow -x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2-9=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9+9 \\
\Leftrightarrow x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(4x^2-713=9x^2+7 \\ \Leftrightarrow 4x^2-9x^2=7+713 \\
\Leftrightarrow -5x^2 = 720 \\
\Leftrightarrow x^2 = \frac{720}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(7x^2-3)=-(20x^2-6) \\ \Leftrightarrow -14x^2+6=-20x^2+6 \\
\Leftrightarrow -14x^2+20x^2=6-6 \\
\Leftrightarrow 6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-4(8x^2-2)=-(39x^2-1583) \\ \Leftrightarrow -32x^2+8=-39x^2+1583 \\
\Leftrightarrow -32x^2+39x^2=1583-8 \\
\Leftrightarrow 7x^2 = 1575 \\
\Leftrightarrow x^2 = \frac{1575}{7}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-3x^2-1023=3x^2-9 \\ \Leftrightarrow -3x^2-3x^2=-9+1023 \\
\Leftrightarrow -6x^2 = 1014 \\
\Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2-1152=0 \\
\Leftrightarrow -8x^2 = 1152 \\
\Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(-8x^2-10)=-(-47x^2-750) \\ \Leftrightarrow 40x^2+50=47x^2+750 \\
\Leftrightarrow 40x^2-47x^2=750-50 \\
\Leftrightarrow -7x^2 = 700 \\
\Leftrightarrow x^2 = \frac{700}{-7} < 0 \\
V = \varnothing \\ -----------------\)