## Aadarsh 3 years ago The number of real roots of (x+3)^4 + (x+5)^4 = 16 is: a) 0 b) 2 c) 4 d) none of these

1. experimentX

2

2. experimentX

-3 and -5

4. experimentX

here's an ugly method http://math.stackexchange.com/questions/785/is-there-a-general-formula-for-solving-4th-degree-equations simplify it to 4th degree equation ... it has at max 4 roots, in our case it's 2 real and 2 complex

@experimentX can u explain the direct solution and step? I didn't get it.

6. Taufique

|dw:1332919098675:dw| the no of solution =cut points of graphs(y=(x+3)^4 and y=16-(x+5)^4)=2 (they are -3 and -5)

But should we do the graph for solving this? Is der no direct method?

8. experimentX

well i must say, @Taufique is quite correct in explaining above ... since curve cuts at two places, it has two real solutions, and two complex solutions

9. Taufique

@Aadarsh you can solve also in this way..

Its ok. But without graph, I want to solve this. please say some other way.

11. experimentX

-5 and -3 are quite visible .. so factorize it (x+3)(x+5)(some terms ..) = 0 ... first find some terms

Can u do and say?

13. experimentX

can you simplify this equation? (x+3)^4 + (x+5)^4 - 16 =0

Not getting exactly. But can we apply Neumark and Ferrari-Langrange method for solving?

15. experimentX

well i guess you can

16. robtobey

$(x+3)^4+(x+5)^4-16=0$$2 (x+3) (x+5) \left(x^2+8 x+23\right)=0$

17. experimentX

well, that what i mean ..!

Oh yeah, I got the factorisation.

19. experimentX

(x2+8x+23) will give you two complex roots, so your real roots are only -5 and -3

20. robtobey

Thank you for the medals.

Most welcome

22. Taufique

First of all , find the dY/dX of the given curve.dy/dx means tangent on the curve. find the cut point of dy/dx and X axis on putting Y=0 in the equation ,and solve it it gives you solution of the equation..

I have not read those concepts. Just completed grade 10. So facing problems.

24. Taufique

ok Aadarsh ji ,i thought that you are in 12 th, you can solve it using hit and trial method.. and factorise this after it..

Ji haan, I solved using trial method, got -5 and -3.

26. Taufique

If you will prepare for iit then you get a complex equation and on that situation it is very tough to guess what is the root...then there is many method to solve such a problem..