Question : If a + b = 5 and a – b = 3, then the value of (a2 + b2) is:
Option 1: 17
Option 2: 18
Option 3: 19
Option 4: 20
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Correct Answer: 17
Solution : Given: a + b = 5 -----------------------(i) a – b = 3 ----------------------(ii) Add both equations (i) and (ii), ⇒ a + b + a – b = 5 + 3 ⇒ 2a = 8 ⇒ a = 4 From equation (i), ⇒ 4 + b = 5 ⇒ b = 5 – 4 ⇒ b = 1 Now, a 2 + b 2 = 4 2 + 1 2 = 16 + 1 = 17 Hence, the correct answer is 17.
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