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Doubt, please help


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Note by Radhesh Sarma
1 year, 10 months ago

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What are you having doubts about? Rahul Saha · 1 year, 10 months ago

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Dear @Sandeep Bhardwaj pls help Radhesh Sarma · 1 year, 10 months ago

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@Radhesh Sarma I think \(\pi\) is the only value satisfying the given equation, when assumed that \([..]\) represents greatest integer function. Sandeep Bhardwaj · 1 year, 10 months ago

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@Sandeep Bhardwaj yes sir, represents greatest integer function. Radhesh Sarma · 1 year, 10 months ago

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@Radhesh Sarma Here is my approach we can write given equation as

\([x] ^{2}-5[x]+6=sin(x) \)

Now we can see that LHS part is always integer. It means \(sin(x) \) can be equal to \(-1,0, 1\).

Further we can see that - 1 and 1 get rejected. This gives 2 solutions \([x]=2, 3\).

This gives \(2 \leq x <4\) In the following range \(sin(x) \) is 0 for only one value of x. That is \(x= \pi\). Shubhendra Singh · 1 year, 10 months ago

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@Shubhendra Singh How do you take out exponent of x outside from G.I.F Akhil Bansal · 1 year, 10 months ago

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@Akhil Bansal Yes you are right, I accept my mistake. Luckily the answer got matched. I'm really sorry:-[ Shubhendra Singh · 1 year, 10 months ago

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@Akhil Bansal he has factorized it Radhesh Sarma · 1 year, 10 months ago

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@Radhesh Sarma Sorry Radhesh, my solution is a bit incorrect. I took \([x]^{2}\) in place of \([x^{2}]\) . So now I think you must try and solve the equation using graph. Shubhendra Singh · 1 year, 10 months ago

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@Shubhendra Singh koi baaat nahi Radhesh Sarma · 1 year, 10 months ago

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@Shubhendra Singh @shubhendra singh ,thank a lot Radhesh Sarma · 1 year, 10 months ago

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@Radhesh Sarma You're welcome 8-) Shubhendra Singh · 1 year, 10 months ago

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