AN Interesting problem

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Find the numebr of solutions of the equation-
8[x² - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F.

#Mathematics #Algebra #Progressions

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2 Answers

466

Himanshu Giria ·2014-06-12 06:06:30

No solution at all...

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Himanshu Giria Because frankly speakingRHS can have values 1'13 &25 only . LHS On the other hand is always a multiple of 4 or 8 or at least even whereas RHS is always odd
Upvote·0· Reply ·2014-06-12 06:11:14
Himanshu Giria As [] always returns an integer...
Upvote·0· Reply ·2014-06-12 06:13:09
Himanshu Giria [â€¦]
Upvote·0· Reply ·2014-06-12 06:13:30
Sushovan Halder yes,your thinking is right.
Upvote·0· Reply ·2014-06-12 10:23:30
Manish Shankar good work Himanshu :)
Upvote·0· Reply ·2014-06-12 23:19:23
Himanshu Giria Thanks Sir...
Upvote·0· Reply ·2014-06-12 23:28:25
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Sushovan Halder ·2014-06-12 10:27:52

Another solution can be:
Let a=[x^2-x];b=[x];c=[sinx].And all of these are integers.so
8a+4b-12c=13
or,2a+b-3c=13/4. LHS is an integer while RHS is not.Hence no solution.

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Manish Shankar good one :)
Upvote·0· Reply ·2014-06-12 23:19:05
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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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AN Interesting problem

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