Question

If 1 2 3 21
X X X
4 9 1
+ 3 = 0, then the value of x is
(a) 3
(b) 0
(c) -1
(d) 1​

Answer 1

Answer:

answer is -1

Step-by-step explanation:

-1 iS the answer

Answer 2

The value of x is - 1

Given :

$\displaystyle\begin{vmatrix} 2 & 3 & 2\\ \sf x & \sf x & \sf x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$

To find :

The value of x is

(a) 3

(b) 0

(c) - 1

(d) 1

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\displaystyle\begin{vmatrix} 2 & 3 & 2\\ \sf x & \sf x & \sf x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$

Step 2 of 2 :

Simplify the given equation

$\displaystyle\begin{vmatrix} 2 & 3 & 2\\ \sf x & \sf x & \sf x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$

$\displaystyle \implies \: \sf x\begin{vmatrix} 2 & 3 & 2\\ \sf 1 & \sf 1& \sf 1 \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$

$\displaystyle \sf\implies \: x[2(1 - 9) - 3(1 - 4) + 2(9 - 4)] + 3 = 0$

$\displaystyle \sf\implies \: x[ - 16 + 9 + 10] + 3 = 0$

$\displaystyle \sf\implies \: 3x + 3 = 0$

Step 3 of 3 :

Find the value of x

$\displaystyle \sf \: 3x + 3 = 0$

$\displaystyle \sf\implies \: 3x = - 3$

$\displaystyle \sf\implies \: x = - 1$

Hence the correct option is (c) - 1

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