Question

if p+q root21 =root 7 + root 3/ root7- root3 then find the value of p and q​

Answer 1

Answer:

$\boxed{ =>p=\frac{5}{2} ,q=\frac{1}{2} }$

Step-by-step explanation:

$=> \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \\\\ rationalising \ factor=\sqrt{7}+\sqrt{3} \\\\ => \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \times \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}+\sqrt{3}} \\\\ => \frac{(\sqrt{7}+\sqrt{3})(\sqrt{7}+\sqrt{3})}{(\sqrt{7}-\sqrt{3})(\sqrt{7}+\sqrt{3})} \\\\ => \frac{(\sqrt{7}+\sqrt{3})^2}{\sqrt{7}^2-\sqrt{3}^2} \\\\ => \frac{\sqrt{7}^2+\sqrt{3}^2+2(\sqrt{7})(\sqrt{3})}{7-3} \\\\ =>\frac{7+3+2\sqrt{21}}{4} \\\\ =>\frac{10+2\sqrt{21}}{4} \\\\ =>\frac{5+\sqrt{21}}{2}$

$=> \frac{5}{2} +\frac{\sqrt{21}}{2} = p+q\sqrt{21} \\\\ =>p=\frac{5}{2} ,q=\frac{1}{2}$

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Formula used :

(a+b)² = a² + b² + 2ab

(a+b) (a-b) = a² - b²

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