Question

appropria
la 1
1 b 1. is positive, then
1 1
C с
(a) abc > 1
(c) abc <-8
(b) abc >-8
(d) abc >-2.
1. If the value of the determinant​

Answer 1

Answer:

Δ=

∣

∣

∣

∣

∣

∣

∣

∣

a

1

1

1

b

1

1

1

c

∣

∣

∣

∣

∣

∣

∣

∣

=abc−(a+b+c)+2

As Δ>0

∴abc+2>a+b+c ...(A)

Using A.M.>G.M.

⇒

3

a+b+c

>(abc)

1/3

or a+b+c>3(abc)

1/3

...(B)

By (A) and (B) we have

abc+2>a+b+c>3(abc)

1/3

⇒abc+2>3(abc)

1/3

⇒2+x

3

>3x(x=(abc)

1/3

)

⇒x

3

−3x+2>0

⇒(x−1)

2

(x+2)>0

∴x>−2

Hence (abc)

1/3

>2

abc>−8