If x⁴ + y⁴ + x²y² = 17 1/16 and x² - xy + y² = 5 1/4 , then one of the values of (x - y) is:

If x⁴ + y⁴ + x²y² = 17 1/16 and x² - xy + y² = 5 1/4…

If x⁴ + y⁴ + x²y² = 17 $\frac{1}{16}$ and x² - xy + y² = 5 $\frac{1}{4}$ , then one of the values of (x - y) is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{5}{2}$

x² - xy + y² = 5 $\frac{1}{4}$ .................(1)

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

(x² + xy + y² ) = (273/16)/(21/4)

(x² + xy + y² ) = 3.25...........(2)

Subtract eq (1) from (2) we get,

-2xy = 2

xy = -1.

Put the value of xy in eq (1) we get,

x² + y² = 21/4 - 1

x² + y² - 2xy + 2xy = 17/4

(x - y)² = 17/4 + 2 = 25/2

x - y = 5/2.