Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4(8x^2+4)=-(-35x^2-124)\)
- \(3x^2+137=-5x^2+9\)
- \(-14x^2+790=-10x^2+6\)
- \(3(4x^2-3)=-(-11x^2+130)\)
- \(3(10x^2+7)=-(-38x^2-13)\)
- \(-5(7x^2-6)=-(33x^2-48)\)
- \(-3x^2-588=0\)
- \(-11x^2-411=-6x^2-6\)
- \(3(8x^2-3)=-(-20x^2-891)\)
- \(2(3x^2+2)=-(-2x^2+140)\)
- \(-4(-3x^2+2)=-(-8x^2+8)\)
- \(5(4x^2-10)=-(-12x^2+50)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4(8x^2+4)=-(-35x^2-124) \\ \Leftrightarrow 32x^2+16=35x^2+124 \\
\Leftrightarrow 32x^2-35x^2=124-16 \\
\Leftrightarrow -3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2+137=-5x^2+9 \\ \Leftrightarrow 3x^2+5x^2=9-137 \\
\Leftrightarrow 8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-14x^2+790=-10x^2+6 \\ \Leftrightarrow -14x^2+10x^2=6-790 \\
\Leftrightarrow -4x^2 = -784 \\
\Leftrightarrow x^2 = \frac{-784}{-4}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(4x^2-3)=-(-11x^2+130) \\ \Leftrightarrow 12x^2-9=11x^2-130 \\
\Leftrightarrow 12x^2-11x^2=-130+9 \\
\Leftrightarrow x^2 = -121 \\
\Leftrightarrow x^2 = \frac{-121}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(10x^2+7)=-(-38x^2-13) \\ \Leftrightarrow 30x^2+21=38x^2+13 \\
\Leftrightarrow 30x^2-38x^2=13-21 \\
\Leftrightarrow -8x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{-8}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-5(7x^2-6)=-(33x^2-48) \\ \Leftrightarrow -35x^2+30=-33x^2+48 \\
\Leftrightarrow -35x^2+33x^2=48-30 \\
\Leftrightarrow -2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2-588=0 \\
\Leftrightarrow -3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2-411=-6x^2-6 \\ \Leftrightarrow -11x^2+6x^2=-6+411 \\
\Leftrightarrow -5x^2 = 405 \\
\Leftrightarrow x^2 = \frac{405}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(8x^2-3)=-(-20x^2-891) \\ \Leftrightarrow 24x^2-9=20x^2+891 \\
\Leftrightarrow 24x^2-20x^2=891+9 \\
\Leftrightarrow 4x^2 = 900 \\
\Leftrightarrow x^2 = \frac{900}{4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(2(3x^2+2)=-(-2x^2+140) \\ \Leftrightarrow 6x^2+4=2x^2-140 \\
\Leftrightarrow 6x^2-2x^2=-140-4 \\
\Leftrightarrow 4x^2 = -144 \\
\Leftrightarrow x^2 = \frac{-144}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-3x^2+2)=-(-8x^2+8) \\ \Leftrightarrow 12x^2-8=8x^2-8 \\
\Leftrightarrow 12x^2-8x^2=-8+8 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(4x^2-10)=-(-12x^2+50) \\ \Leftrightarrow 20x^2-50=12x^2-50 \\
\Leftrightarrow 20x^2-12x^2=-50+50 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)