Let the number 2,b,c be in an A.P. and A = [1&1&1 2&b&c 4&b2&c2] .If det (A)∈[2,16] , then c lies in the interval :

Question

Let the number 2,b,c be in an A.P. and A = [1&1&1 2&b&c 4&b2&c2] .If det (A)∈[2,16] , then c lies in the interval : (A) [2,3) (B) (2 + 23/4 , 4) (C) [3, 2 + 23/4 ] (D) [4, 6 ]

Tardigrade Admin · Accepted Answer

put b = (2+c/2) in determinant of A |A| =(c3-6c2+12c-8/4) ∈[2,16] ⇒ (c-2)3 ∈[8,64] ⇒ c ∈ [4,6]

Q. Let the number 2,b,c be in an A.P. and $A = ⎣ ⎡ 124 1 b b^{2} 1 c c^{2} ⎦ ⎤$ .If det $(A) \in [2, 16]$ , then c lies in the interval :

[2,3)

$(2 + 2^{3/4}, 4)$

$[3, 2 + 2^{3/4}]$

[4, 6 ]

put $b = \frac{2 + c}{2}$ in determinant of A
$∣ A ∣ = \frac{c ^{3} - 6 c ^{2} + 12 c - 8}{4} \in [2, 16]$
$\Rightarrow (c - 2)^{3} \in [8, 64]$
$\Rightarrow c \in [4, 6]$

Q. Let the number 2,b,c be in an A.P. and A=⎣⎡​124​1bb2​1cc2​⎦⎤​ .If det (A)∈[2,16] , then c lies in the interval :

[2,3)

(2+23/4,4)

[3,2+23/4]

[4, 6 ]

put b=22+c​ in determinant of A ∣A∣=4c3−6c2+12c−8​∈[2,16] ⇒(c−2)3∈[8,64] ⇒c∈[4,6]

Q. Let the number 2,b,c be in an A.P. and $A = ⎣ ⎡ 124 1 b b^{2} 1 c c^{2} ⎦ ⎤$ .If det $(A) \in [2, 16]$ , then c lies in the interval :

$(2 + 2^{3/4}, 4)$

$[3, 2 + 2^{3/4}]$

put $b = \frac{2 + c}{2}$ in determinant of A
$∣ A ∣ = \frac{c ^{3} - 6 c ^{2} + 12 c - 8}{4} \in [2, 16]$
$\Rightarrow (c - 2)^{3} \in [8, 64]$
$\Rightarrow c \in [4, 6]$