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JAMB Mathematics 2020 Paper

Question : 40

Total: 40

Find the non-zero positive value of x which satisfies the equation

Solution:

Concept:

Find the determinant of the given

3\times3

matrix, set it to zero, and solve for

x

Explanation:

\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{vmatrix}=0

Expanding along the first row:

x\begin{vmatrix}x&1\\1&x\end{vmatrix}-1\begin{vmatrix}1&1\\0&x\end{vmatrix}=0

x(x^2-1)-1(x)=0

x^3-x-x=0

x^3-2x=0

x(x^2-2)=0

x=0

x^2=2

The non-zero positive value is

x=\sqrt{2}

Answer:

\sqrt{2}

(Option C).

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