If x- y = $\sqrt {5}$ 10 + xy =&

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If x- y = $\sqrt {5}$

10 + xy = $\frac{13}{xy}$

find x⁴ + y⁴ + 10

Options:

Correct Answer:

Explanation:

x- y = $\sqrt {5}$

x² + y² = 5 + 2xy

x⁴ + y⁴ = 25 + 4x²y² + 20xy - 2x²y²

x⁴ + y⁴ = 25 + 2x²y² + 20xy

= 25 + 2xy(xy + 10)

= 25 + 2xy × $\frac{13}{xy}$

x⁴ + y⁴ = 51

x⁴ + y⁴ +10 = 61