Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+304=5x^2+4\)
2. \(2(-6x^2+9)=-(7x^2+702)\)
3. \(4x^2-16=0\)
4. \(x^2+225=0\)
5. \(-5(5x^2-7)=-(27x^2+357)\)
6. \(2(2x^2+5)=-(2x^2-304)\)
7. \(7x^2+448=0\)
8. \(-2x^2-89=-8x^2+7\)
9. \(-2(-10x^2-2)=-(-26x^2-154)\)
10. \(-10x^2+2=-7x^2+2\)
11. \(10x^2-220=9x^2+5\)
12. \(-5(-7x^2-9)=-(-41x^2+555)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+304=5x^2+4 \\ \Leftrightarrow 2x^2-5x^2=4-304 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(2(-6x^2+9)=-(7x^2+702) \\ \Leftrightarrow -12x^2+18=-7x^2-702 \\ \Leftrightarrow -12x^2+7x^2=-702-18 \\ \Leftrightarrow -5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{-5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(4x^2-16=0 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(x^2+225=0 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-5(5x^2-7)=-(27x^2+357) \\ \Leftrightarrow -25x^2+35=-27x^2-357 \\ \Leftrightarrow -25x^2+27x^2=-357-35 \\ \Leftrightarrow 2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(2(2x^2+5)=-(2x^2-304) \\ \Leftrightarrow 4x^2+10=-2x^2+304 \\ \Leftrightarrow 4x^2+2x^2=304-10 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(7x^2+448=0 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-2x^2-89=-8x^2+7 \\ \Leftrightarrow -2x^2+8x^2=7+89 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(-2(-10x^2-2)=-(-26x^2-154) \\ \Leftrightarrow 20x^2+4=26x^2+154 \\ \Leftrightarrow 20x^2-26x^2=154-4 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-10x^2+2=-7x^2+2 \\ \Leftrightarrow -10x^2+7x^2=2-2 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(10x^2-220=9x^2+5 \\ \Leftrightarrow 10x^2-9x^2=5+220 \\ \Leftrightarrow x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(-5(-7x^2-9)=-(-41x^2+555) \\ \Leftrightarrow 35x^2+45=41x^2-555 \\ \Leftrightarrow 35x^2-41x^2=-555-45 \\ \Leftrightarrow -6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{-6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)