Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?
Option 1: 8
Option 2: 12
Option 3: 4
Option 4: 6
Answer (1)
24th Jan, 2024
Correct Answer: 6
Solution :
Given: $x^2-x y+y^2=7$ -----------(i)
Also, $x^4+x^2 y^2+y^4=133$
⇒ $(x^2-x y+y^2)(x^2+x y+y^2) = 133$
⇒ $7(x^2+x y+y^2) = 133$
⇒ $x^2+x y+y^2 = 19$ ------------(ii)
Subtracting (i) from (ii),
$2xy = 19-7$
⇒ $xy = 6$
Hence, the correct answer is 6.
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