**Question**

**Explanation**

If

*a*+*b*= 11, then 2*ab*= (*a*+*b*)² – (*a*² +*b*²) = 121 – 100 = 21. But 2*ab*is an even number, whereas 21 is odd. This is a*contradiction*. So (B) is impossible. ©**Remarks**

Short and sweet isn’t it? This uses the square-of-sum identity (

*a*+*b*)² =*a*² + 2*ab*+*b*². I used the tactic of assuming the answer is correct [H08] and showing that this leads to something nonsensical [H05]. So the original assumption must be wrong. This is called “*proof by contradiction*” or*reductio ad absurdum*(in Latin).
By the way, the correct
answer option is (E) from the Pythagorean Triplet 8² + 6²
= 10² with {

*a*,*b*} = {8, 6}. The question seems to be taken from some Kangaroo mathematics competition.
H05. Work backwards

H08. Make suppositions

H09. Restate the problem in
another way

H13* Use Equation / write a
Mathematical Sentence

**Suitable Levels**

*****Lower Secondary Mathematics competition

*****GCE ‘O’ Level “Elementary” Mathematics (challenge)

* other syllabuses that involve whole
numbers and Pythagorean triplets

* any precocious or independent learner who
loves a challenge

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