Question

If |2x 3||-5 x|=|4 3||-5 8| the negative value of x

Answer 1

Step-by-step explanation:

Given that:

$\left|\begin{array}{cc}2x&3\\-5&x\end{array}\right|=\left|\begin{array}{cc}4&3\\-5&8\end{array}\right|$

To find: Negative value of x

Solution: To find Negative value of x,first one have to solve(open) the determinant from both sides

$2 {x}^{2} + 15 = 32 + 15 \\ \\ 2 {x}^{2} = 32 \\ \\ {x}^{2} = \frac{32}{2} \\ \\ {x}^{2} = 16 \\ \\ x = \sqrt{16} \\ \\ x = ± 4$

Here x have two values x= 4 and x=-4.

So, negative value of x is -4.

Hope it helps you.

Answer 2

Determinants

Given.

$\left|\begin{array}{cc}2x&3\\-5&x\end{array}\right|=\left|\begin{array}{cc}4&3\\-5&8\end{array}\right|$

To find. the negative value of x

Solution.

Now,

$\left|\begin{array}{cc}2x&3\\-5&x\end{array}\right|=\left|\begin{array}{cc}4&3\\-5&8\end{array}\right|$

Expand both sides along the first row:

$\quad 2x^{2}+15=32+15$

$\Rightarrow 2x^{2}=32$

$\Rightarrow x^{2}=16$

$\Rightarrow x=\pm 16$

Answer. therefore the negative value of x is 4.

Note. A different view arises in the problem when we compare like terms from both sides (x = 2, x = 8), but this is a determinant problem, so we take its values only without thinking about equating both sides.