Mathematics
Consider the following two statements :
Statement 1: If a + b = 0, then a2 + b2 = 0
Statement 2: a2 + b2 = (a + b)2.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Expansions
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Answer
Given,
⇒ a + b = 0
Squaring both sides, we get
⇒ (a + b)2 = 02
⇒ a2 + b2 + 2ab = 0
⇒ a2 + b2 = -2ab
∴ Statement 1 is false.
(a + b)2 = a2 + b2 + 2ab
∴ Statement 2 is false.
∴ Both statements are false.
Hence, option 2 is the correct option.
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