If x = √10 + √3 and y = √10 - √3, then find x² + y².
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Correct answer: A
Explanation
Given:
x = √10 + √3
y = √10 − √3
By the formula:
(a + b)² = a² + b² + 2ab
(a − b)² = a² + b² − 2ab
x² = (√10 + √3)²
= 10 + 3 + 2√30
= 13 + 2√30
y² = (√10 − √3)²
= 10 + 3 − 2√30
= 13 − 2√30
x² + y² = (13 + 2√30) + (13 − 2√30) = 26