Question

If x = 7 +4 3 then the value of x + 1/x

is​

Answer 1

Answer:

x + (1/x) = 14

Step-by-step explanation:

We have,

x = 7 + 4√3

Then,

(1/x) = [1/(7 + 4√3)]

Rationalizing the denominator,

= [1/(7 + 4√3)] × (7 - 4√3)/(7 - 4√3)

= [1 × (7 - 4√3)]/[(7 + 4√3)(7 - 4√3)]

= [7 - 4√3]/[(7 + 4√3)(7 - 4√3)]

Using the identity,

(a + b)(a - b) = a² - b²

= [7 - 4√3]/[7² - (4√3)²]

= [7 - 4√3]/[49 - (4²√3²)]

= [7 - 4√3]/[49 - (16 × 3)]

= [7 - 4√3]/[49 - 48]

= [7 - 4√3]/1

= 7 - 4√3

∴ (1/x) = 7 - 4√3

Then,

x + (1/x) = [7 + 4√3] + [7 - 4√3]

x + (1/x) = 7 + 4√3 + 7 - 4√3

∴ x + (1/x) = 14

Hope it helped and believing you understood it........All the best

Answer 2

Given ×=7-4 3----(1)

=1/7-4 3

=7+4 3/(7-4 3)(7+4 3)

=7+ 4 3/7²-(4 3)²

=7+4 3/49-48

=7+4 3----(2)

now,

the value of ×+1/×

=7-4 3+7+4 3

=14

therefore,.

the value of ×+1/×=14