Question

simplify it by rationalising the denominator.
please answer it correctly.​

Answer 1

Solution :-

Rationalizing the Denominator of First Part :-

→ [(7 - √5) / (7 + √5) ] * [(7 - √5) / (7 - √5) ]

using (a + b)(a - b) = a² - b² in Denominator,

→ [(7 - √5)² / {(7)² - (√5)²} ]

using (a - b)² = a² + b² - 2ab in Numerator,

→ [ ( 49 + 5 - 14√5 ) / (49 - 5) ]

→ (54 - 14√5) / 44

→ 2(27 - 7√5) /44

→ (27 - 7√5) / 22

_____________________

Similarly, Rationalizing the Denominator of second Part :-

→ [(7 + √5) / (7 - √5) ] * [(7 + √5) / (7 + √5) ]

using (a + b)(a - b) = a² - b² in Denominator,

→ [(7 + √5)² / {(7)² - (√5)²} ]

using (a + b)² = a² + b² + 2ab in Numerator,

→ [ ( 49 + 5 + 14√5 ) / (49 - 5) ]

→ (54 + 14√5) / 44

→ 2(27 + 7√5)/ 44

→ (27 + 7√5) / 22

___________________

Subtracting Both Part Now, we get :-

→ [ (27 - 7√5) / 22 ] - [ (27 + 7√5) / 22 ]

→ [ { 27 - 7√5 - (27 + 7√5) } / 22 ]

→ [ { 27 - 7√5 - 27 - 7√5 } / 22 ]

→ [ (-14√5) / 22 ]

→ (-7√5) / 11 (Ans).

Answer 2

The entire solution is in the attachment......