Simplification....at its worst.
We all are very familiar with the simplification of a + b ± 2 a b , which is a ± b (for a > b ). But can you simplify this? 9 − 7 7 Express your answer in the form of a − b , where a > b and enter the value of 2 a + 1 0 b .
The answer is 46.
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1 solution
Cool and quick solution! My brute force approach (summarized below) was much more tedious. I should really look for shortcuts more.
9 − 7 7 = a − b , then 9 − 7 7 = a + b − 2 a b .
a + b = 9 and − 2 a b = − 7 7 ⇒ a b = 4 7 7 .
a 2 − 9 a + 4 7 7 = 0 ⇒ a or b = 2 1 1 , 2 7 .
⇒ 2 a + 1 0 b = 2 ⋅ 2 1 1 + 1 0 ⋅ 2 7 = 1 1 + 3 5 = 4 6 .
Why is it : Simplification at it's worst ? Isn't this question easy ?
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Idk, I took a loooooong time to think of an answer for this one :P
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Okay . Are you planning on posting some Trigonometry problems ? Also are you going to participate in OPC 3 ?
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@A Former Brilliant Member – Trigonometry occasionally, maybe, but not continuously. What's OPC 3? Never heard of it.
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@Omkar Kulkarni – See this .
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@A Former Brilliant Member – Ohh. I might! I'm not so good at geometry, and especially not good at proofs. But thanks for notifying!
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@Omkar Kulkarni – What's the harm in trying ? It's not like everyone will see your solution , only Rajdeep will see it .
Btw , it's alright . Do take part in OPC 4 !
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@A Former Brilliant Member – Yup! I will try, of course
Did it the same way..Cool :)
9 − 7 7
= 2 1 8 − 2 7 7
= 2 ( 1 1 ) 2 − 2 ( 1 1 ) ( 7 ) + ( 7 ) 2
= 2 ( 1 1 − 7 ) 2
= 2 1 1 − 2 7