Question

If x + √15 = 4 , then what is x + 1/x?

Answer 1

Answer:

8

Step-by-step explanation:

x + √15 = 4

x = 4 - √15

1/x = 1/(4- √15)

Rationalizing,

1/x = 4+ √15/ (4-√15)(4+√15) = 4+ √15/(16-15) = 4+ √15

x+ 1/x = 4- √15 + 4+ √15 = 8

Answer 2

SOLUTION ✍️

x + √15 = 4

x = 4 - √15

NOW

1/x = 1/(4 - √15)

• Rationalising the denominator

1/x = [1/(4 - √15)] × [(4 + √15)/(4 + √15)]

1/x = (4 + √15) / [(4 - √15)(4 + √15)]

1/x = (4 + √15) / (4)² - (√15)²

1/x = (4 + √15) / 16 - 15

1/x = 4 + √15

THEREFORE

» x + 1/x = 4 - √15 + 4 + √15 = 8

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