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If x = √5 + √3 and y = √5 - √3 then the value of (x4 – y4) is
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- 64 √15
- 16
- 544
- 32 √15
- 64 √15
Correct Option: A
x = √5 + √3
x2 = ( √5 + √3 )2
x2 = 5 + 3 + 2√15 = 8 + 2√15
and y = √5 - √3
y2 = ( √5 - √3 )2
y2 = 8 - 2√15
∴ x4 – y4 = (x2 + y2)(x + y)(x - y)
⇒ x4 – y4 = (8 + 2√15 + 8 - 2√15) × (√5 + √3 + √5 - √3) × (√5 + √3 - √5 + √3)
⇒ x4 – y4 = 16 × 2√5 × 2√3 = 64√15
