CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Which of the following values of α satisfy the equation
∣ ∣ ∣(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2∣ ∣ ∣=648α?


A
-4
loader
B
9
loader
C
-9
loader
D
4
loader

Solution

The correct options are
B 9
C -9
Given determinant could be expressed as product of two determinants.
i.e. ∣ ∣ ∣(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2∣ ∣ ∣=648α
 ∣ ∣ ∣1+2α+α21+4α+4α21+6α+9α24+4α+α24+8α+4α24+12α+9α29+6α+α29+12α+4α29+18α+9α2∣ ∣ ∣=648α
 ∣ ∣ ∣1αα242αα293αα2∣ ∣ ∣.∣ ∣111246149∣ ∣=648 α α3∣ ∣111421931∣ ∣.∣ ∣111246149∣ ∣=648α
     8α3=648α    α381α=0α(α281)=0      α=0, ±9

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More



footer-image