Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2-64=0\)
- \(-2(4x^2+5)=-(10x^2-88)\)
- \(-3(-2x^2-9)=-(-13x^2+1156)\)
- \(-5(-4x^2+4)=-(-17x^2+452)\)
- \(-7x^2+112=0\)
- \(2(4x^2-3)=-(-3x^2+6)\)
- \(8x^2+1568=0\)
- \(10x^2-1179=3x^2+4\)
- \(-4(-9x^2-6)=-(-31x^2-1004)\)
- \(4(-9x^2-3)=-(44x^2-1140)\)
- \(11x^2+1=6x^2-4\)
- \(6x^2-384=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2-64=0 \\
\Leftrightarrow 4x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-2(4x^2+5)=-(10x^2-88) \\ \Leftrightarrow -8x^2-10=-10x^2+88 \\
\Leftrightarrow -8x^2+10x^2=88+10 \\
\Leftrightarrow 2x^2 = 98 \\
\Leftrightarrow x^2 = \frac{98}{2}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-3(-2x^2-9)=-(-13x^2+1156) \\ \Leftrightarrow 6x^2+27=13x^2-1156 \\
\Leftrightarrow 6x^2-13x^2=-1156-27 \\
\Leftrightarrow -7x^2 = -1183 \\
\Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-5(-4x^2+4)=-(-17x^2+452) \\ \Leftrightarrow 20x^2-20=17x^2-452 \\
\Leftrightarrow 20x^2-17x^2=-452+20 \\
\Leftrightarrow 3x^2 = -432 \\
\Leftrightarrow x^2 = \frac{-432}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2+112=0 \\
\Leftrightarrow -7x^2 = -112 \\
\Leftrightarrow x^2 = \frac{-112}{-7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2(4x^2-3)=-(-3x^2+6) \\ \Leftrightarrow 8x^2-6=3x^2-6 \\
\Leftrightarrow 8x^2-3x^2=-6+6 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(8x^2+1568=0 \\
\Leftrightarrow 8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(10x^2-1179=3x^2+4 \\ \Leftrightarrow 10x^2-3x^2=4+1179 \\
\Leftrightarrow 7x^2 = 1183 \\
\Leftrightarrow x^2 = \frac{1183}{7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-4(-9x^2-6)=-(-31x^2-1004) \\ \Leftrightarrow 36x^2+24=31x^2+1004 \\
\Leftrightarrow 36x^2-31x^2=1004-24 \\
\Leftrightarrow 5x^2 = 980 \\
\Leftrightarrow x^2 = \frac{980}{5}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4(-9x^2-3)=-(44x^2-1140) \\ \Leftrightarrow -36x^2-12=-44x^2+1140 \\
\Leftrightarrow -36x^2+44x^2=1140+12 \\
\Leftrightarrow 8x^2 = 1152 \\
\Leftrightarrow x^2 = \frac{1152}{8}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(11x^2+1=6x^2-4 \\ \Leftrightarrow 11x^2-6x^2=-4-1 \\
\Leftrightarrow 5x^2 = -5 \\
\Leftrightarrow x^2 = \frac{-5}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-384=0 \\
\Leftrightarrow 6x^2 = 384 \\
\Leftrightarrow x^2 = \frac{384}{6}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)