Question

x=4+square root of 15 then find the value of (x+1/x) to the power 2​

Answer 1

Notice that 4² and 15 differ by only 1. This will be useful to find the inverse of x.

→ 1/x

→ 1/(4 + √15)

→ Multiply (4 - √15)/(4 - √15).

→ (4-√15)/(4² - 15)

∴1/x = 4 - √15

∴x + 1/x = 8

Therefore, the answer is 8² or 64.

Answer 2

1/x

1/(4 + √15)

Multiply (4 - √15)/(4 - √15).

(4-√15)/(4² - 15)

∴1/x = 4 - √15

∴x + 1/x = 8

Therefore, the answer is 8² or 64

Hope this helps you.