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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
 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
 2 years ago

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

experimentXBest ResponseYou've already chosen the best response.1
here'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
 2 years ago

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

TaufiqueBest ResponseYou've already chosen the best response.3
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)
 2 years ago

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

experimentXBest ResponseYou've already chosen the best response.1
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
 2 years ago

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

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

experimentXBest ResponseYou've already chosen the best response.1
5 and 3 are quite visible .. so factorize it (x+3)(x+5)(some terms ..) = 0 ... first find some terms
 2 years ago

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

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

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

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

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

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

experimentXBest 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
 2 years ago

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

TaufiqueBest ResponseYou've already chosen the best response.3
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..
 2 years ago

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

TaufiqueBest ResponseYou've already chosen the best response.3
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..
 2 years ago

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

TaufiqueBest ResponseYou've already chosen the best response.3
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..
 2 years ago

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