Question

Write $x^2$ + 2$\sqrt{3}$ x + 3 as $x^2$+ p x+ q x + 3 such that p+q = 2$\sqrt{3}$ and pq = 3

If p=$\sqrt{a}$ , q= $\sqrt{b}$ . What is the value of a + b ?

Answer 1

Multiply 1 with 3 and we get 3

Pairs of 3 that include $\sqrt{3}$ are

$\sqrt{3}$ x $\sqrt{3}$ = 3 sum $\sqrt{3}$+ $\sqrt{3}$ = 2$\sqrt{3}$

-$\sqrt{3}$ x - $\sqrt{3}$ = 3 sum -$\sqrt{3}$ - $\sqrt{3}$ = - 2$\sqrt{3}$

So our required pair is √3 and√3

$x^2$+ $\sqrt{3}$x+ $\sqrt{3}$x + 3

p = $\sqrt{3}$ , q =$\sqrt{3}$

p = $\sqrt{a}$ , q =$\sqrt{b}$

$\sqrt{3}$ = $\sqrt{a}$ , $\sqrt{3}$ = $\sqrt{b}$

3 = a , 3 = b

So, a + b = 6