Question

If $a$ and $b$ are the roots of the equation $x^2-5x+6=0$. Find the value of $\frac{a^2+b^2+ab}{|a^2-b^2|}$?

• A. $-20$
• B. $7$
• C. $\frac{19}{5}$
• D. None of these

Answer 1

The correct option is C $\frac{19}{5}$

Given that:

$x^2-5x+6=0$ and $a$ and $b$ are roots of the equation.

To find:

$\frac{a^2+b^2+ab}{|a^2-b^2|}=?$

Solution:

$x^2-5x+6=0$

$x^2-3x-2x+6=0$

$(x-3)(x-2)=0$

$x=3$ or $x=2$

So, let $a=3$ and $b=2$

$\frac{a^2+b^2+ab}{|a^2-b^2|}=\frac{3^2+2^2+3\times 2}{|3^2-2^2|}=\frac{19}{5}$

And if $a=2$ and $b=3$ then also

$\frac{a^2+b^2+ab}{|a^2-b^2|}=\frac{2^2+3^2+2\times 3}{|2^2-3^2|}=\frac{19}{5}$

Hence, C is the correct option.