Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(5x^2-10)=-(17x^2+462)\)
2. \(5(-6x^2+3)=-(38x^2-23)\)
3. \(7x^2+343=0\)
4. \(5x^2+125=0\)
5. \(-7x^2+448=0\)
6. \(-10x^2+14=-7x^2+2\)
7. \(-6x^2+384=0\)
8. \(x^2-53=6x^2-8\)
9. \(6x^2-1350=0\)
10. \(-4(2x^2+9)=-(3x^2-944)\)
11. \(3x^2-286=-3x^2+8\)
12. \(-10x^2-190=-2x^2+10\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(5x^2-10)=-(17x^2+462) \\ \Leftrightarrow -25x^2+50=-17x^2-462 \\ \Leftrightarrow -25x^2+17x^2=-462-50 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(5(-6x^2+3)=-(38x^2-23) \\ \Leftrightarrow -30x^2+15=-38x^2+23 \\ \Leftrightarrow -30x^2+38x^2=23-15 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(7x^2+343=0 \\ \Leftrightarrow 7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5x^2+125=0 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2+448=0 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(-10x^2+14=-7x^2+2 \\ \Leftrightarrow -10x^2+7x^2=2-14 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(x^2-53=6x^2-8 \\ \Leftrightarrow x^2-6x^2=-8+53 \\ \Leftrightarrow -5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(6x^2-1350=0 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(-4(2x^2+9)=-(3x^2-944) \\ \Leftrightarrow -8x^2-36=-3x^2+944 \\ \Leftrightarrow -8x^2+3x^2=944+36 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(3x^2-286=-3x^2+8 \\ \Leftrightarrow 3x^2+3x^2=8+286 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-10x^2-190=-2x^2+10 \\ \Leftrightarrow -10x^2+2x^2=10+190 \\ \Leftrightarrow -8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-8} < 0 \\ V = \varnothing \\ -----------------\)