If x4 + x2y2 + y4 = 273 x2 -

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x⁴ + x²y² + y⁴ = 273

x² - xy + y² = 13, then

find xy.

Options:

Correct Answer:

Explanation:

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

⇒ 273 = 13 × (x²+ y² + xy)

⇒ x²+ y² + xy = \(\frac{273}{13}\)

⇒ x²+ y² + xy = 21 ............(i)

⇒ x²+ y² - xy = 13 (given) .............(ii)

(i) - (ii),

⇒ 2xy = 8

⇒ xy = 4