Question

已知a=(-3,-2),b=(-4,k),若(5a-b)·(b-3a)=-55,求实数K的值.急急急····全过程,谢

Answer 1

(5a-b)·(b-3a)=-55

5ab-15a^2-b^2+3ab=-55

8ab-15a^2-b^2=-55

8(-3*(-4)+(-2)*k)-15*((-3)^2+(-2)^2)-((-4)^2+k^2)=-55

8(12-2k)-15*13-(16+k^2)=-55

96-16k-195-16-k^2=-55

k^2+16k+44=0

k=(-16±4√5)/2

k=2√5-8或 k=-2√5-8