If [ cc a+b & 2 5 & a b ]= [ ll 6 & 2 5 & 8 ], then find the valu… - Vidyadip

MCQ

If $\left[\begin{array}{cc}a+b & 2 \\ 5 & a b\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$, then find the values of $a$ and $b$ respectively.

A
2,4
B
4,2
✓
Both (a) and (b)
D
None of these

✓

Answer

Correct option: C.

Both (a) and (b)

(c) : Since, $\left[\begin{array}{cc}a+b & 2 \\ 5 & a b\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$
$\Rightarrow a+b=6$ and $a b=8$
$\Rightarrow \quad a+\frac{8}{a}=6$ $(\because a b=8 \Rightarrow b=8 / a)$
$\Rightarrow a^2-6 a+8=0 \Rightarrow(a-2)(a-4)=0 \Rightarrow a=2,4$
Hence, $a=2, b=4$ or $a=4, b=2$

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