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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