Question

Solve 1/( 5 −2√3) +1 /( 5+2√3)

Answer 1

ANSWER:

${ \sf{ \frac{1}{5 - 2\sqrt{3} } + \frac{1}{5 + 2 \sqrt{3} } }}$

Taking LCM

$= {\sf{ \frac{(5 + 2 \sqrt{3} ) + (5 - 2 \sqrt{3}) }{(5 - 2 \sqrt{3})(5 - 2 \sqrt{3} ) } }}$

Using

(a + b)(a - b) = a² - b²

${ \sf{ = \frac{5 + \cancel{2 \sqrt{3}} + 5 - \cancel{2 \sqrt{3} } }{ {5}^{2} - ( { 2 \sqrt{3} )}^{2} } }}$

${ \sf{ = \frac{10}{25 - 12} }}$

$= \frac{10}{13}$

MORE INFORMATION:

→ (a + b)² = a² + 2ab + b²

→ (a + b)(a - b) = a² - b²

→ (a - b)² = a² - 2ab + b²

→ (a + b)² - (a - b)² = 4ab

→ (a + b)² + (a - b)² = 2(a² + b²)

CONCEPT USED:

→ Surds