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Yahoo!

  • one year ago

The number of solutions for 9x^2 - 30x + 37 = 9sin2x ?

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  1. Yahoo!
    • one year ago
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    @hartnn @satellite73 @RadEn

  2. satellite73
    • one year ago
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    graph em they don't intersect

  3. hba
    • one year ago
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    http://www.wolframalpha.com/input/?i=9x%5E2+-+30x+%2B+37+%3D+9sin2x Have a look at this.

  4. Yahoo!
    • one year ago
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    Is there any way to find it manually i mean...With out Graph...:)

  5. Taufique
    • one year ago
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    yes there is a way to find the number of real solution of given equation::: step1: let y=9x^2 - 30x + 37 step2: and let y=9sin2x step 3: plot the graph of both equation in the same axis .. step 4: the point of intersection of the both curve will give the number of real solution of the given equation..

  6. tkhunny
    • one year ago
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    Complete the square on the left hand side. What is the minimum value of that expression?

  7. satellite73
    • one year ago
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    that wont quite do it

  8. satellite73
    • one year ago
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    oh yes it will, sorry

  9. Taufique
    • one year ago
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    y=9x^2 - 30x + 37 this is the eqn of parabola so draw the graph of this parabola. and y=9sin2x is a sine curve which maximum value will be 9 and minimum value will be -9 .and also draw it.

  10. satellite73
    • one year ago
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    @tkhunny has a method without the graph min is too large,

  11. satellite73
    • one year ago
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    but this will not work in general, because it could be that the min value of the parabola is less that the max of the sine curve, but they still could not intersect

  12. tkhunny
    • one year ago
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    True. I thought it might be a good first clue.

  13. Taufique
    • one year ago
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    \[12\le9x ^{2}-30x+37\] and \[-9 \le \sin 2x \le 9\] wee see that te two curve will never intersect to each other

  14. tkhunny
    • one year ago
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    @Taufique typo. "9*" missing from the sine expression.

  15. Taufique
    • one year ago
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    ohh sorry ..yes ,9 is missing in the above equation

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