Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

5 problems

1.Positive integers m and n satisfy

Find

2.Find the positive integer n such that

3.A trapezoid has side lengths

and

in some order. Find its area

4.A rectangle with integer side lengths has the property that its area minus 5 times its perimeter equals

Find the minimum possible perimeter of this rectangle.

5.For real numbers a, b, and c, the roots of the polynomial

form an
arithmetic progression. Find

Last edited by tony123 (2024-03-14 21:20:40)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,298

Re: 5 problems

Thanks Tony,

More (hopefully) later.

Bob

ps. Still stuck with http://www.mathisfunforum.com/viewtopic.php?pid=432520#p432520

Maybe I need a little hint please.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,298

Re: 5 problems

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

For Q4, is it the area minus (5 times the perimeter),

As in A - 5P = 2023

Or is it (the area minus 5) times the perimeter,

As in (A - 5) * P = 2023

I'm guessing it's the first one??

Last edited by Keep_Relentless (2024-05-08 23:03:09)

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

Last edited by Keep_Relentless (2024-05-08 23:02:32)

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

Oh I forgot the sides are integers.

Last edited by Keep_Relentless (2024-05-08 23:32:24)

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

I think for Q3 you use Brahmagupta's formula

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

Regarding Q5, help is needed on finding roots of quintic equations and what's needed to see the answer, thanks

Last edited by Keep_Relentless (2024-05-09 00:33:29)

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 43

Re: 5 problems

Can anyone show how to do Q5??

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,298

Re: 5 problems

I called the roots a, a+d, a+2d, a+3d and a+4d and expanded that quintic. There were things about the resulting expression that suggested a + b  + c = 9, but I'm not confident that's the correct answer so this one is still on my 'to-do list'.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob