If x4 + x2y2 + y4 = 21, x2 +

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x⁴ + x²y² + y⁴ = 21,

x² + xy + y² = 3, then

find 4xy.

Options:

-4

-8

Correct Answer:

-8

Explanation:

Formula → x⁴ + y⁴ + x²y² = (x²+ y² + xy) × (x²+ y² - xy)

⇒ 21 = 3 × (x²+ y² - xy)

⇒ x²+ y² - xy = \(\frac{21}{3}\) = 7 .........(i)

⇒ x²+ y² + xy = 3 (given) .............(ii)

Now, (ii) - (i)

⇒ 2xy = - 4

⇒ 4xy = -8