x + y = 5; xy = 6 হলে, এবং x > y হলে, x5 + y5 এর মান কত?

A 275

B 243

C 32

D 36

Solution

Correct Answer: Option A

x+y=5
⇒ (x + y)² = 25
⇒ (x - y)² + 4xy = 25
⇒ (x - y)² + 4.6=25
⇒ (x - y)² = 1
∴ x-y=1

এখন,
x+y=5
x=y=1
------------
2x = 6
∴ x =3
∴ y = 2

এখন,
x² + y² = (3)5 + (2)5
= 243 +32 = 275


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