Question

7. Simplify the following by rationalizing the denominator.
(i) 4+√5/ 4-√5
+
4-√5 / 4+√5

Answer 1

Step-by-step explanation:

1. 4+√5 /4-√5 + 4 -√5 /4+√5

4+√5 /4 -√5 × 4+√5/ 4+√5

= (4+√5)²/ 4²-√5²

= 16 +5 + 8√5 / 16 - 5

= 21 +8√5 / 11 --------- (i)

4-√5 /4+√5 × 4-√5 / 4-√5

= (4 -√5)² / (4²-√5²)

= (16 +5 -8√5) / 16 -5)

= (21 - 8√5) / 11. --------- (ii)

21 + 8√5 +21 -8√5

------------------------------------

11

= 21 +21

------------- = 42/11

11