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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