Question

The product of two numbers is $4.$ If one of the numbers is $\sqrt{7}–\sqrt{3},$ then the other number is .

Answer 1

Let the other number be $x.$

$⟹x\times (\sqrt{7}–\sqrt{3})=4$

$⟹x=\frac{4}{\sqrt{7}–\sqrt{3}}$

$⟹x=\frac{4}{\sqrt{7}–\sqrt{3}}\times \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}+\sqrt{3}}$

$⟹x=\frac{4\times (\sqrt{7}+\sqrt{3})}{(\sqrt{7}{)}^2–(\sqrt{3}{)}^2}$

$(\because (a–b\left)\right(a+b)=a^2–b^2)$

$x=\frac{4\times (\sqrt{7}+\sqrt{3})}{7–3}$

$x=\frac{4\times (\sqrt{7}+\sqrt{3})}{4}$

$⟹x=\sqrt{7}+\sqrt{3}$