Question : If x + y = 7 and xy = 19, calculate the value of x2 + y2.
Option 1: 17
Option 2: 12
Option 3: 11
Option 4: 19
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Correct Answer: 11
Solution : Given: x + y = 7 and xy = 19. On squaring both sides of the equation x + y = 7, we get, (x + y) 2 = 7 2 ⇒ (x 2 + y 2 + 2xy) = 49 ⇒ x 2 + y 2 + 2 × 19 = 49 ⇒ x 2 + y 2 = 49 – 38 $\therefore$ x 2 + y 2 = 11 Hence, the correct answer is 11.
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