Correct Answer - Option 3 : 248
Given:
x + y = 2√5
xy = 2
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
According to the question,
⇒ x + y = 2√5
Squaring both sides,
⇒ (x + y)2 = (2√5)2
⇒ x2 + y2 + 2xy = 20
⇒ x2 + y2 + 2(2) = 20
⇒ x2 + y2 = 20 – 4
⇒ x2 + y2 = 16
Squaring both sides,
⇒ (x2 + y2)2 = 162
⇒ x4 + y4 + 2x2y2 = 256
⇒ x4 + y4 + 2(2)2 = 256
⇒ x4 + y4 + 8 = 256
⇒ x4 + y4 = 256 – 8
⇒ x4 + y4 = 248
∴ The value of x4 + y4 is 248.
