Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(5(5x^2-5)=-(-22x^2-218)\)
- \(4x^2+96=5x^2-4\)
- \(-x^2-1=0\)
- \(-5(-5x^2+4)=-(-22x^2+212)\)
- \(x^2-196=0\)
- \(-4(-6x^2+9)=-(-19x^2-209)\)
- \(-3(10x^2-8)=-(33x^2-216)\)
- \(-12x^2+1347=-4x^2-5\)
- \(-13x^2+654=-5x^2+6\)
- \(3(10x^2-9)=-(-28x^2-365)\)
- \(4x^2-83=7x^2-8\)
- \(-3(4x^2-5)=-(5x^2+13)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(5(5x^2-5)=-(-22x^2-218) \\ \Leftrightarrow 25x^2-25=22x^2+218 \\
\Leftrightarrow 25x^2-22x^2=218+25 \\
\Leftrightarrow 3x^2 = 243 \\
\Leftrightarrow x^2 = \frac{243}{3}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(4x^2+96=5x^2-4 \\ \Leftrightarrow 4x^2-5x^2=-4-96 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-x^2-1=0 \\
\Leftrightarrow -x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(-5x^2+4)=-(-22x^2+212) \\ \Leftrightarrow 25x^2-20=22x^2-212 \\
\Leftrightarrow 25x^2-22x^2=-212+20 \\
\Leftrightarrow 3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-196=0 \\
\Leftrightarrow x^2 = 196 \\
\Leftrightarrow x^2 = \frac{196}{1}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-4(-6x^2+9)=-(-19x^2-209) \\ \Leftrightarrow 24x^2-36=19x^2+209 \\
\Leftrightarrow 24x^2-19x^2=209+36 \\
\Leftrightarrow 5x^2 = 245 \\
\Leftrightarrow x^2 = \frac{245}{5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-3(10x^2-8)=-(33x^2-216) \\ \Leftrightarrow -30x^2+24=-33x^2+216 \\
\Leftrightarrow -30x^2+33x^2=216-24 \\
\Leftrightarrow 3x^2 = 192 \\
\Leftrightarrow x^2 = \frac{192}{3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-12x^2+1347=-4x^2-5 \\ \Leftrightarrow -12x^2+4x^2=-5-1347 \\
\Leftrightarrow -8x^2 = -1352 \\
\Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-13x^2+654=-5x^2+6 \\ \Leftrightarrow -13x^2+5x^2=6-654 \\
\Leftrightarrow -8x^2 = -648 \\
\Leftrightarrow x^2 = \frac{-648}{-8}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(3(10x^2-9)=-(-28x^2-365) \\ \Leftrightarrow 30x^2-27=28x^2+365 \\
\Leftrightarrow 30x^2-28x^2=365+27 \\
\Leftrightarrow 2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4x^2-83=7x^2-8 \\ \Leftrightarrow 4x^2-7x^2=-8+83 \\
\Leftrightarrow -3x^2 = 75 \\
\Leftrightarrow x^2 = \frac{75}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(4x^2-5)=-(5x^2+13) \\ \Leftrightarrow -12x^2+15=-5x^2-13 \\
\Leftrightarrow -12x^2+5x^2=-13-15 \\
\Leftrightarrow -7x^2 = -28 \\
\Leftrightarrow x^2 = \frac{-28}{-7}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)