2nd DAY: SOLVE THIS INTERESTING PROBLEM...

IT'S THE SECOND DAY OF POSTING AND DISCUSSING VARIOUS MATH PROBLEMS THAT I EVENTUALLY COME ACROSS.....HAPPY SOLVING...:-)*

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

since m and l are real .it means that l<1 and m<1.(as if they were greater than 1 the square of the other would be complex)

hence write l = cosx (for some x)

and m is the sin x

then divide al+bm=c by sqrta^2+b^2 (As a^2 + b^2 is not 0)

write the lhs as sin(j+x) (for some j)

hence as the sin function oscillates between -1 and 1

c oscillates between -sqrt a^2 + b^2 to sqrt a^2+b^2

i know i didnt write clearly but hope u get what im saying

pranav chakravarthy - 8 years, 1 month ago

yea, i got to what you are trying to say......it's great and right.....a good job...then wait for tomorrow for an another great problem......keep in touch....:--]

Sayan Chaudhuri - 8 years, 1 month ago

The answer is a

pranav chakravarthy - 8 years, 1 month ago

how got to answer.....?..... :-o

Sayan Chaudhuri - 8 years, 1 month ago

It can be seen through this... most of the above portion ... an expression of the form {Asinx +(or -) Bcosx} oscillates between +(-) sqrt(a^2 + b^2) ...

Saloni Gupta - 8 years, 1 month ago

@Saloni Gupta – yes u r right.....Pranav c. himself described it rightly.......:)

Sayan Chaudhuri - 8 years, 1 month ago

using cauchy-schwarz inequality,we have (a^2+b^2)(l^2+m^2)>=(al+bm)^2=c^2,which implies A

Sauvik Mondal - 8 years, 1 month ago

good idea......you are then showing acumen over problem solving....great application...thanx.....

Sayan Chaudhuri - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$