If x⁴ + y⁴ + x²y² = 117 and x² + y² - xy = 3(4 + √(3) ), then the value of (x² + y²) will be:

If x⁴ + y⁴ + x²y² = 117 and x² + y² - xy = 3(4 + √(3) )…

If x⁴ + y⁴ + x²y² = 117 and x² + y² - xy = 3(4 + $\sqrt{3}$ ), then the value of (x² + y²) will be:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 12.

$(x^2 + y^2 - xy)(x^2 + y^2 +xy) = x^4 + y^4 + x^2y^2$

x² + y² - xy = 3(4 + √3) ----(i)

(x² + y² +xy) = 117/3(4 + √3) = 39 × (4 - √3)/ (4 + √3) × (4 - √3)

⇒ 12 - 3√3 ----(ii)

By adding (i) & (ii)

2(x² + y²) = 12 + 3√3 + 12 - 3√3

∴ (x² + y²) = 12