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

1.	X=4+square root of 15 then find the value of (x+1/x) to the power 2
Answer» 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»

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.

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

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