If (x/y) + (y/x) = √7 then what is the value of (x4/y4) + (y4/x4) ?
Solution
Correct Answer: Option B
দেওয়া আছে, (x/y) + (y/x) = √7
∴ x4/y4 + y4/x4
= (x/y)4 + (y/x)4
= {(x/y)2}2 + {(y/x)2}2
= {(x/y)2 + (y/x)2}2 - 2.(x2/y2).(y2/x2)
= {(x/y)2 + (y/x)2}2 - 2
= [{(x/y) + (y/x)}2 - 2.(x/y).(y/x)]2 - 2
= {(√7)2 - 2}2 - 2
= (7 - 2)2 - 2
= 52 - 2
= 25 - 2
= 23
∴ x4/y4 + y4/x4
= (x/y)4 + (y/x)4
= {(x/y)2}2 + {(y/x)2}2
= {(x/y)2 + (y/x)2}2 - 2.(x2/y2).(y2/x2)
= {(x/y)2 + (y/x)2}2 - 2
= [{(x/y) + (y/x)}2 - 2.(x/y).(y/x)]2 - 2
= {(√7)2 - 2}2 - 2
= (7 - 2)2 - 2
= 52 - 2
= 25 - 2
= 23
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