Question

plz answer both these questions​

Answer 1

Answer:

1)a = 6+2√3

1/a = 1/6+2√3

→ = 1/6+2√3 × 6-2√3/6-2√3

→ = (6-2√3)/(6+2√3)(6-2√3)

→ = (6-2√3)/(6²-(2√3)²)

→ = (6-2√3)/(36-4(3))

→ = (6-2√3)/(36-12)

→ = (6-2√3)/24

★a-1/a

→ 6+2√3 - (6-2√3)/24

→ {24(6+2√3) - 6 + 2√3}/24

→ {144+48√3-6+2√3}/24

→ {138+50√3}/24

→ 138/24 + 50√3/24

→ 23/4 + 25√3/12

→ {69+25√3}/12

→ {69+√1875}/12

→ 3{23+√625}/12

→ {23+25}/4

= 48/4

=12

2)

x = 7 + √40

=5 + 2 + 2√10 = (√5 + √2)²

√x = √5 + √2

1/√x = 1/(√5 + √2) = (√5 - √2)/((√5 + √2)(√5 - √2) = (√5 - √2)/(5 - 2) = (√5 - √2)/3

√x + 1/√x = √5 + √2 + (√5 - √2)/3 = (2/3)(2√5 + √2)