Question

Prove that if x2— 4 = 0, then x = 0 by contradiction method.

Answer 1

Answer:

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Answer 2

GIVEN:- x²— 4 = 0

TO FIND:- Prove x = 0

SOLUTION:-

• In mathematics, proof by contradiction is a means of proof that ascertains the truth or the fact of a proposition, by showing that assuming the proposition to be false leads to a contradiction.

• To prove by method contradiction, we first assume that the statement is false.

${x}^{2} - 4 = 0$

• Assuming x = 0

• Adding 4 both sides

${x}^{2} - 4 + 4 = 0 + 4$

${x}^{2} = 4$

• Square rooting both the sides

$\sqrt{ {x}^{2} } = \sqrt{4} \\ x = 2$

• Therefore our assumption is correct.

Hence, we prove the statement.

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