Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-17x^2+1576=-9x^2+8\)
- \(5(4x^2-7)=-(-15x^2-810)\)
- \(-4x^2-154=-6x^2+8\)
- \(14x^2-1123=9x^2+2\)
- \(-5(5x^2+2)=-(32x^2-333)\)
- \(-9x^2+438=-2x^2-10\)
- \(5x^2+87=10x^2+7\)
- \(-10x^2+246=-8x^2+4\)
- \(-3(-10x^2-7)=-(-33x^2-69)\)
- \(-11x^2+10=-8x^2+10\)
- \(10x^2-5=3x^2-5\)
- \(-6x^2-600=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-17x^2+1576=-9x^2+8 \\ \Leftrightarrow -17x^2+9x^2=8-1576 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(5(4x^2-7)=-(-15x^2-810) \\ \Leftrightarrow 20x^2-35=15x^2+810 \\
\Leftrightarrow 20x^2-15x^2=810+35 \\
\Leftrightarrow 5x^2 = 845 \\
\Leftrightarrow x^2 = \frac{845}{5}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-4x^2-154=-6x^2+8 \\ \Leftrightarrow -4x^2+6x^2=8+154 \\
\Leftrightarrow 2x^2 = 162 \\
\Leftrightarrow x^2 = \frac{162}{2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(14x^2-1123=9x^2+2 \\ \Leftrightarrow 14x^2-9x^2=2+1123 \\
\Leftrightarrow 5x^2 = 1125 \\
\Leftrightarrow x^2 = \frac{1125}{5}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-5(5x^2+2)=-(32x^2-333) \\ \Leftrightarrow -25x^2-10=-32x^2+333 \\
\Leftrightarrow -25x^2+32x^2=333+10 \\
\Leftrightarrow 7x^2 = 343 \\
\Leftrightarrow x^2 = \frac{343}{7}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-9x^2+438=-2x^2-10 \\ \Leftrightarrow -9x^2+2x^2=-10-438 \\
\Leftrightarrow -7x^2 = -448 \\
\Leftrightarrow x^2 = \frac{-448}{-7}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(5x^2+87=10x^2+7 \\ \Leftrightarrow 5x^2-10x^2=7-87 \\
\Leftrightarrow -5x^2 = -80 \\
\Leftrightarrow x^2 = \frac{-80}{-5}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-10x^2+246=-8x^2+4 \\ \Leftrightarrow -10x^2+8x^2=4-246 \\
\Leftrightarrow -2x^2 = -242 \\
\Leftrightarrow x^2 = \frac{-242}{-2}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-3(-10x^2-7)=-(-33x^2-69) \\ \Leftrightarrow 30x^2+21=33x^2+69 \\
\Leftrightarrow 30x^2-33x^2=69-21 \\
\Leftrightarrow -3x^2 = 48 \\
\Leftrightarrow x^2 = \frac{48}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+10=-8x^2+10 \\ \Leftrightarrow -11x^2+8x^2=10-10 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(10x^2-5=3x^2-5 \\ \Leftrightarrow 10x^2-3x^2=-5+5 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-6x^2-600=0 \\
\Leftrightarrow -6x^2 = 600 \\
\Leftrightarrow x^2 = \frac{600}{-6} < 0 \\
V = \varnothing \\ -----------------\)