Question

If x = √5 − √2/

√5 + √2

and xy = 1 , find the value of x2 + xy + y2

.​

Answer 1

Step-by-step explanation:

x²+1+y² =0

x²+y²=-1

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Answer 2

Step-by-step explanation:

• GIVEN THAT •

✓ The value of

$x = \sqrt{5} - \sqrt{2}$

✓ The value of

$y = \sqrt{5} + \sqrt{2}$

✓ The value of

$xy = 1$

• TO FIND •

✓ The value of

${x}^{2} + xy \: + {y}^{2}$

• SOLUTION •

${x}^{2} + xy + {y}^{2} \\ = {( \sqrt{5} - \sqrt{2} ) }^{2} + 1 + {( \sqrt{5} + \sqrt{2}) }^{2} \\ = {( \sqrt{5} )}^{2} + {( \sqrt{2}) }^{2} - 2 \times \sqrt{5} \times \sqrt{2} + 1 + {( \sqrt{5}) }^{2} + {( \sqrt{2} )}^{2} + 2 \times \sqrt{5} \times \sqrt{2} \\ = 5 + 2 + 1 + 5 + 2 \\ = 15$

• CONCLUSION •

✓ Answer:- The value of

${x}^{2} + xy + {y}^{2}$

= 15