Question

simply 1/√5+√2 +1/√5-√2 write answer step by step​

Answer 1

ANSWER:

To Simplify:

$\:\:\:\:\bullet\:\:\:\:\dfrac{1}{\sqrt{5}+\sqrt{2}}+\dfrac{1}{\sqrt{5}-\sqrt{2}}$

Solution:

$\text{We are given that,}\\\\:\longrightarrow\dfrac{1}{\sqrt{5}+\sqrt{2}}+\dfrac{1}{\sqrt{5}-\sqrt{2}}\\\\\text{Taking LCM,}\\\\:\implies\dfrac{(\sqrt{5}-\sqrt{2})+(\sqrt{5}+\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}\\\\\text{We know that,}\\\\:\hookrightarrow(a+b)(a-b)=a^2-b^2\\\\\text{So,}\\\\:\implies\dfrac{\sqrt{5}-\sqrt{2}\!\!\!/+\sqrt{5}+\sqrt{2}\!\!\!/}{(\sqrt{5})^2-(\sqrt{2})^2}\\\\\text{Adding the \sqrt5s }\\\\:\implies\dfrac{2\sqrt5}{5-2}\\\\\bf{:\implies\dfrac{2\sqrt5}{3}}$

$\text{Hence,}\\\\\bf{:\implies\dfrac{1}{\sqrt{5}+\sqrt{2}}+\dfrac{1}{\sqrt{5}-\sqrt{2}}=\dfrac{2\sqrt5}{3}}$

Formula Used:

• (a + b)(a - b) = a² - b²

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identities}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$