Question

solve x²+(√a-√b)x-√a√b by using the formula -b±√b²-4ac/2a

Answer 1

Answer:

Solving discriminant first: b^2 - 4ac( in eq. )

= > ( $\sqrt a$ - $\sqrt b$ )^2 - 4(1)(-$\sqrt a$$\sqrt b$)

= > ($\sqrt a$)^2 + ($\sqrt b$)^2 - 2$\sqrt a$$\sqrt b$ + 4$\sqrt a$$\sqrt b$

= > ($\sqrt a$)^2 + ($\sqrt b$)^2 + 2$\sqrt a$$\sqrt b$

= > ( $\sqrt a$ + $\sqrt b$ )^2

Now,

= > [ -($\sqrt a$-$\sqrt b$)$\pm$$\sqrt(\sqrt a+\sqrt b)^2$ ]/2

= > [ - $\sqrt a$ + $\sqrt b$ + $\sqrt a$ + $\sqrt b$ ] / 2 or [ -$\sqrt a$ + $\sqrt b$ - $\sqrt a$ - $\sqrt b$ ] / 2

= > 2$\sqrt b$/2 or - 2$\sqrt a$/2

= > $\sqrt b$ or - $\sqrt a$

Hence, x = $\sqrt b$ or - $\sqrt a$