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The number of solutions for 9x^2 - 30x + 37 = 9sin2x ?
@hartnn @satellite73 @RadEn
graph em they don't intersect
http://www.wolframalpha.com/input/?i=9x%5E2+-+30x+%2B+37+%3D+9sin2x Have a look at this.
Is there any way to find it manually i mean...With out Graph...:)
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..
Complete the square on the left hand side. What is the minimum value of that expression?
that wont quite do it
oh yes it will, sorry
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.
@tkhunny has a method without the graph min is too large,
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
True. I thought it might be a good first clue.
\[12\le9x ^{2}-30x+37\] and \[-9 \le \sin 2x \le 9\] wee see that te two curve will never intersect to each other
@Taufique typo. "9*" missing from the sine expression.
ohh sorry ..yes ,9 is missing in the above equation