Question

simplify 1/7+4 root 3 + 1/7-4 root 3​

Answer 1

Answer:

= 14

Step-by-step explanation:

$=> \frac{1}{7+4\sqrt{3}} \\ \\ rationalising \ factor=7-4\sqrt{3} \\\\ => \frac{1}{7+4\sqrt{3}} \times \frac{7-4\sqrt{3}}{7-4\sqrt{3}} \\\\ => \frac{7-4\sqrt{3}}{(7+4\sqrt{3})(7-4\sqrt{3})} \\\\ => \frac{7-4\sqrt{3}}{7^2-(4\sqrt{3})^2} \\\\ =>\frac{7-4\sqrt{3}}{49-16(3)} \\\\ => \frac{7-4\sqrt{3}}{49-48} \\\\ =>\frac{7-4\sqrt{3}}{1} \\\\ => 7-4\sqrt{3}$

$=> \frac{1}{7-4\sqrt{3}} \\ \\ rationalising \ factor=7+4\sqrt{3} \\\\ => \frac{1}{7-4\sqrt{3}} \times \frac{7+4\sqrt{3}}{7+4\sqrt{3}} \\\\ => \frac{7+4\sqrt{3}}{(7-4\sqrt{3})(7+4\sqrt{3})} \\\\ => \frac{7+4\sqrt{3}}{7^2-(4\sqrt{3})^2} \\\\ =>\frac{7+4\sqrt{3}}{49-16(3)} \\\\ => \frac{7+4\sqrt{3}}{49-48} \\\\ =>\frac{7+4\sqrt{3}}{1} \\\\ => 7+4\sqrt{3}$

$=> \frac{1}{7+4\sqrt{3}} + \frac{1}{7-4\sqrt{3}} \\\\ =>7-4\sqrt{3} +7+4\sqrt{3} \\\\ =>7+7 \\\\ =>14$