## Yahoo! 2 years ago The number of solutions for 9x^2 - 30x + 37 = 9sin2x ?

1. Yahoo!

2. satellite73

graph em they don't intersect

3. hba

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

4. Yahoo!

Is there any way to find it manually i mean...With out Graph...:)

5. Taufique

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

Complete the square on the left hand side. What is the minimum value of that expression?

7. satellite73

that wont quite do it

8. satellite73

oh yes it will, sorry

9. Taufique

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

@tkhunny has a method without the graph min is too large,

11. satellite73

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

True. I thought it might be a good first clue.

13. Taufique

$12\le9x ^{2}-30x+37$ and $-9 \le \sin 2x \le 9$ wee see that te two curve will never intersect to each other

14. tkhunny

@Taufique typo. "9*" missing from the sine expression.

15. Taufique

ohh sorry ..yes ,9 is missing in the above equation