Question

Find the value of 'x' if, *
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Answer 1

Answer:

The value of  $x=$ ±$6$

Step-by-step explanation:

Given the two determinants are equal.

Therefore we have to calculate the two determinants separately.

$det\left[\begin{array}{ccc}2x&5\\8&x\\\end{array}\right]=2x^{2} -40$

$det\left[\begin{array}{ccc}6&-2\\7&3\\\end{array}\right]=18+14=32$

since the two determinants are equal, we can write

$2x^{2} -40=32$

(rearranging)

$2x^{2} =32+40=72\\ x^{2} =72/2=36$

therefore  $x=6 or -6$

Thank you

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of x if

$\displaystyle\begin{vmatrix} \sf 2x & 5 \\ 8 & \sf x \end{vmatrix} = \displaystyle\begin{vmatrix} 6 & - 2 \\ 7 & 3 \end{vmatrix}$

(a) 3

(b) 6 , - 6

(c) 3 , - 3

(d) 6

EVALUATION

Here the given equation is

$\displaystyle\begin{vmatrix} \sf 2x & 5 \\ 8 & \sf x \end{vmatrix} = \displaystyle\begin{vmatrix} 6 & - 2 \\ 7 & 3 \end{vmatrix}$

We find the value of x as below

$\displaystyle\begin{vmatrix} \sf 2x & 5 \\ 8 & \sf x \end{vmatrix} = \displaystyle\begin{vmatrix} 6 & - 2 \\ 7 & 3 \end{vmatrix}$

$\displaystyle \sf{ \implies 2 {x}^{2} - 40 = 18 + 14 }$

$\displaystyle \sf{ \implies 2 {x}^{2} - 40 = 32 }$

$\displaystyle \sf{ \implies 2 {x}^{2} = 72 }$

$\displaystyle \sf{ \implies {x}^{2} = 36 }$

$\displaystyle \sf{ \implies x = \pm \: 6 }$

FINAL ANSWER

Hence the correct option is (b) 6 , - 6

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