Solve : |(x-2, 2x-3, 3x-4), (x-4, 2x-9, ...

Solve : `|(x-2, 2x-3, 3x-4), (x-4, 2x-9, 3x-16) ,(x-8 ,2x-27,3x-64)|=0`

Text Solution

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To solve the given determinant equation, we need to find the value of \( x \) such that: \[ \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix} = 0 ...

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Using properties of determinants, solve the following for x: |[x-2, 2x-3, 3x-4],[x-4, 2x-9, 3x-16],[ x-8, 2x-27, 3x-64]|=0

(i) Solve the equation |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,2x-64):}|=0 (ii) Prove that x = 1 is a root of the equation (ii) Prove that x=1 is a root of the following equation |{:(x+1,3,5),(2,x+2,5),(2,3,x+4):}|=0 Also find the remaining roots. (iii) If a+b+c=0 then solve |{:(a-x,c,b),(c,b-x,a),(v,a,c-x):}|=0 (iv) Solve |{:(6-x,3,3),(3,4-x,5),(3,5,4-5):}|=0

Knowledge Check

If |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)| = 0 , then x =

A

1

B

2

C

3

D

4

Solve: x-(2x-(3x-4)/7)=(4x-27)/3-3 .

A

2

B

4

C

3

D

6

Let D(x)=|{:(x^2+4x-3, 2x+4,13),(2x^2+5x-9,4x+5,26),(8x^2-16x+1, 16x-6, 104):}|=alphax^3+betax^2 + gammax+delta then :

A

`alpha+beta=0`

B

`beta+gamma=0`

C

`alpha+beta+gamma+delta=0`

D

`alpha + beta+ gamma =0`

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Solve for xdet[[x-2,2x-3,3xx-4x-4,2x-9,3x-16x-8,2x-27,3x-64]]=0

Solve: the [[x-2.2x-3.3x-4x-4.2x-9.3x-16x-8.2x-27.3x-64]] = 0

Solve for x: (x-2)/4+2x=3x+10

x-(2x-(3x-4)/(7))=(4x-27)/(3)-3

Solve for x: (8x-1)/2+3x-4=(1+2x)/3

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