if [a+b&2 5&ab] = [6&2 5&8], then find the values of a and b respectively

Question

if [a+b&2 5&ab] = [6&2 5&8], then find the values of a and b respectively (A)  2,4  (B)  4,2  (C) Both (a) (b) (D) None of these

Tardigrade Admin · Accepted Answer

since [a+b&2 5&ab] = [6&2 5&8] ⇒ a+ b = 6 and ab = 8 ⇒ a+( 8/a ) = 6 (∴ ab = 8 ⇒ b =(8 / a)) ⇒ a2 - 6a + 8 = 0 ⇒ (a - 2) (a - 4) = 0 ⇒ a =2,4 hence, a=2, b = 4, or a = 4 , b=2

Q. if $[a + b 5 2 ab] = [6528]$ , then find the values of a and b respectively

$2, 4$

$4, 2$

Both (a) & (b)

None of these

since $[a + b 5 2 ab] = [6528]$
$\Rightarrow a + b = 6$ and $ab = 8$
$\Rightarrow a + \frac{8}{a} = 6 (∴ ab = 8 \Rightarrow b = \frac{8}{a})$
$\Rightarrow a^{2} - 6 a + 8 = 0$
$\Rightarrow (a - 2) (a - 4) = 0$
$\Rightarrow a = 2, 4$
hence, $a = 2, b = 4$ , or $a = 4, b = 2$

Q. if [a+b5​2ab​]=[65​28​], then find the values of a and b respectively

2,4

4,2