chalte chalte find the no. of solutions

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find the no of solutions

x+y+z=24
x²+y²+z²=210
xyz=440

a.1
b.2
c.3
d.infinite

#Mathematics #Algebra

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5 Answers

62

Lokesh Verma ·2009-10-22 07:30:04

find xy+yz+zx = 366/2 = 183

So the cubic equation that will have roots as x, y , z will be

t³-24t²+183t-440 = 0

For which you have to find the number of solutions..

can you pull this off?

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1

Grandmaster ·2009-10-24 03:02:57

bada hefty hai......found in 1 of open test's q paper.....

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39

Pritish Chakraborty ·2009-10-24 09:12:07

The roots of the cubic are 11,5 and 8. So I guess that makes it 3 solutions?

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62

Lokesh Verma ·2009-10-25 22:16:27

No pritish...

I think it will be very tough to "guess the roots"

Ofcourse there are integer roots here so guessing the roots is very easy using factors of the constant term...

BUt For a more general way, you should try and find the maxima and minima of the function (local)

Can someone use this hint?

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11

Devil ·2009-10-25 22:17:58

Isn't it the same as b555's qsn - posted a few days earlier?

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