Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2(-5x^2-8)=-(-4x^2-232)\)
- \(9x^2+228=10x^2+3\)
- \(-4x^2-144=0\)
- \(-10x^2+145=-4x^2-5\)
- \(5(10x^2-8)=-(-47x^2-548)\)
- \(5(4x^2+4)=-(-25x^2+0)\)
- \(4(10x^2-4)=-(-35x^2+11)\)
- \(-11x^2+48=-6x^2+3\)
- \(-3x^2+588=0\)
- \(4(-10x^2+10)=-(48x^2-40)\)
- \(-3(-6x^2-6)=-(-23x^2-38)\)
- \(3(6x^2-9)=-(-16x^2+25)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2(-5x^2-8)=-(-4x^2-232) \\ \Leftrightarrow 10x^2+16=4x^2+232 \\
\Leftrightarrow 10x^2-4x^2=232-16 \\
\Leftrightarrow 6x^2 = 216 \\
\Leftrightarrow x^2 = \frac{216}{6}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(9x^2+228=10x^2+3 \\ \Leftrightarrow 9x^2-10x^2=3-228 \\
\Leftrightarrow -x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{-1}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-4x^2-144=0 \\
\Leftrightarrow -4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-10x^2+145=-4x^2-5 \\ \Leftrightarrow -10x^2+4x^2=-5-145 \\
\Leftrightarrow -6x^2 = -150 \\
\Leftrightarrow x^2 = \frac{-150}{-6}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(5(10x^2-8)=-(-47x^2-548) \\ \Leftrightarrow 50x^2-40=47x^2+548 \\
\Leftrightarrow 50x^2-47x^2=548+40 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(5(4x^2+4)=-(-25x^2+0) \\ \Leftrightarrow 20x^2+20=25x^2+0 \\
\Leftrightarrow 20x^2-25x^2=0-20 \\
\Leftrightarrow -5x^2 = -20 \\
\Leftrightarrow x^2 = \frac{-20}{-5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(4(10x^2-4)=-(-35x^2+11) \\ \Leftrightarrow 40x^2-16=35x^2-11 \\
\Leftrightarrow 40x^2-35x^2=-11+16 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-11x^2+48=-6x^2+3 \\ \Leftrightarrow -11x^2+6x^2=3-48 \\
\Leftrightarrow -5x^2 = -45 \\
\Leftrightarrow x^2 = \frac{-45}{-5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-3x^2+588=0 \\
\Leftrightarrow -3x^2 = -588 \\
\Leftrightarrow x^2 = \frac{-588}{-3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4(-10x^2+10)=-(48x^2-40) \\ \Leftrightarrow -40x^2+40=-48x^2+40 \\
\Leftrightarrow -40x^2+48x^2=40-40 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3(-6x^2-6)=-(-23x^2-38) \\ \Leftrightarrow 18x^2+18=23x^2+38 \\
\Leftrightarrow 18x^2-23x^2=38-18 \\
\Leftrightarrow -5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(6x^2-9)=-(-16x^2+25) \\ \Leftrightarrow 18x^2-27=16x^2-25 \\
\Leftrightarrow 18x^2-16x^2=-25+27 \\
\Leftrightarrow 2x^2 = 2 \\
\Leftrightarrow x^2 = \frac{2}{2}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)