α dan β adalah akar – akar persamaan kuadrat x2 + 3x + K = 0 jika α2 – β2 = 21, maka nilai K adalah

x²+3x+k = 0
x1² - x2² =21
(x1-x2)(x1+x2)= √D/ a *-b/a
x1² - x2² = -√D * b / a²
21 = - √b²-4ac *b /1²
21= √9-4(1)(K) * -3
-7= √9-4k
49= 9-4K
K=40/-4 = -10

Maaf kalau salah :)

[tex]\displaystyle p^2-q^2=21\\(p-q)(p+q)=21\\\left(\pm\frac{\sqrt{D}}{a}\right)\left(-\frac{b}{a}\right)=21\\\left(\pm\frac{\sqrt{b^2-4ac}}{a}\right)\left(-\frac{b}{a}\right)=21\\\left(\pm\frac{\sqrt{3^2-4(1)k}}{1}\right)\left(-\frac{3}{1}\right)=21\\\pm\sqrt{9-4k}=-7\\9-4k=49\\-4k=40\\\boxed{\boxed{k=-10}}[/tex]