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 2 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
 2 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

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Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Please say the detailed steps.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1here's an ugly method http://math.stackexchange.com/questions/785/isthereageneralformulaforsolving4thdegreeequations simplify it to 4th degree equation ... it has at max 4 roots, in our case it's 2 real and 2 complex

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0@experimentX can u explain the direct solution and step? I didn't get it.

Taufique
 2 years ago
Best ResponseYou've already chosen the best response.3dw: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)

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0But should we do the graph for solving this? Is der no direct method?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1well 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

Taufique
 2 years ago
Best ResponseYou've already chosen the best response.3@Aadarsh you can solve also in this way..

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Its ok. But without graph, I want to solve this. please say some other way.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.15 and 3 are quite visible .. so factorize it (x+3)(x+5)(some terms ..) = 0 ... first find some terms

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1can you simplify this equation? (x+3)^4 + (x+5)^4  16 =0

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Not getting exactly. But can we apply Neumark and FerrariLangrange method for solving?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1well i guess you can

robtobey
 2 years ago
Best ResponseYou've already chosen the best response.0\[(x+3)^4+(x+5)^416=0 \]\[2 (x+3) (x+5) \left(x^2+8 x+23\right)=0 \]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1well, that what i mean ..!

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Oh yeah, I got the factorisation.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1(x2+8x+23) will give you two complex roots, so your real roots are only 5 and 3

robtobey
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you for the medals.

Taufique
 2 years ago
Best ResponseYou've already chosen the best response.3First 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..

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0I have not read those concepts. Just completed grade 10. So facing problems.

Taufique
 2 years ago
Best ResponseYou've already chosen the best response.3ok Aadarsh ji ,i thought that you are in 12 th, you can solve it using hit and trial method.. and factorise this after it..

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Ji haan, I solved using trial method, got 5 and 3.

Taufique
 2 years ago
Best ResponseYou've already chosen the best response.3If 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..

Aadarsh
 2 years ago
Best ResponseYou've already chosen the best response.0Really? Yeah preparing for IIT
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