Question

What is the value of m,if square root 12 raise to 3m-2=12 square
1)0 2)1 3)2 4)4​

Answer 1

Answer:

x4−(3m+2)x2+m2=0

Let the roots be,

β+d,β−d,β+3d,β−3d

x4+0x2−(3m+2)x2+0x+m2=0

⇒0=(β−3d)+(β−d)+(β+3d)+(β+d)=4β

⇒β=0

−(3m+2)=(−d)(d)+(−d)(3d)+(−d)(−3d)+(d)(3d)+(d)(−3d)+(3d)(−3d)

⇒−(3m+2)=−d2−3d2+3d2+3d2−3d2−9d2=−10d2

⇒103m+2​=d2

m2=(−3d)(3d)(−d)(d)=9d4

⇒m2=9100(3m+2)2​

⇒100m2=9(9m2+12m+4)

⇒0=−10m2+108m+36

⇒m=6,m=−196​