If $x^4 + x^2y^2 + y^4 = 133$ and $x^2 -

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x^4 + x^2y^2 + y^4 = 133$ and $x^2 - xy + y^2 = 7$, then what is the value of xy?

Options:

Correct Answer:

Explanation:

If $x^4 + x^2y^2 + y^4 = 133$

$x^2 - xy + y^2 = 7$--- (1)

what is the value of xy?

x⁴ + x²y² + y⁴ = (x²– xy + y²) (x² + xy + y²)

Then , $x^2 + xy + y^2 = \frac{133}{7}$ = 19----- (2)

From equation 1 and 2 we get,

xy = 6