Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi Relentless and bobbym,

The solution #2656 is correct! Neat work, Relentless and bobbym!

#2657. Solve:

,

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi bobbym,

The solution #2657 is correct! Neat work!

#2658. Solve:

(i) x + y = 14 and x - y = 4.
(ii) 0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi bobbym,

The solutions in #2658 (two solution sets) are correct! Excellent!

#2659. Solve:

and

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi bobbym,

The solution #2659 is correct! Neat work!

#2660. A fraction becomes

, if 2 is added to both numerator and denominator. If 3 is added to both the numerator and the denominator it becomes

. Find the fraction.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hello!
This one is straightforward, but hey, it's Christmas!

Last edited by Relentless (2015-12-25 00:19:13)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi Relentless and bobbym,

The solution #2660 is correct! Good work, Relentless and bobbym!

#2661. If the polynomial

is divided by

, the remainder comes out to be (x + a), find 'k' and 'a'.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

bobbym,
Your answer makes x a complex number. Is that intended?

If I have interpreted the problem correctly, I think the answer is sought in terms of x, because there are heaps of possible solutions, even over the integers

Last edited by Relentless (2015-12-25 21:38:05)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Oral puzzles

Hi bobbym and Relentless,

I too get the same solution as bobbym did! Excellent!

#2662. Find the other zeroes of the polynomial

if it is given that two of its zeroes are

and

.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

I must have misinterpreted the question then, lol (:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

Hi Relentless;

The solution given for 2661 works for all x.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hey bobbym;
Evidently, but I don't see how it works ;S

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Hi;

When you divide the two polys given you get:

So you need to make 2k - 9 equal to 1 to get the desired form.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Hm. For some reason when I am dividing I am getting a very complicated result, and when I multiply what you gave by the denominator to check it, I also get an arduous result.

Is it not true that (x^2-2x+k)(k^2+(2k-9)x-8k+10) expands out to k^3+k^2 x^2-8 k^2+2 k x^3-12 k x^2+7 k x+10 k-9 x^3+28 x^2-20 x, which is not at all what the numerator was?
I am quite flabbergasted about it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

Is it not true that (x^2-2x+k)(k^2+(2k-9)x-8k+10) expands out to k^3+k^2 x^2-8 k^2+2 k x^3-12 k x^2+7 k x+10 k-9 x^3+28 x^2-20 x, which is not at all what the numerator was?

Why should it equal the numerator?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Because the result of a division multiplied by the denominator has to equal the numerator? x/y = z -> x = yz
Is that what has happened here? :S :S

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

What you are saying is rarely true. When we divide 10 by 5 and get 2 we can now say 2 * 5 = 10. But when we divide 11 by 5 we get 2 r 1. Neither 5 *2 equals 11 or 5 * 1.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

At this rate, I will be bamboozled into oblivion. 11/5 = 2.2, and 5*2.2 clearly equals 11

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Oral puzzles

We are not working with decimals here. The poly

is a remainder.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Oral puzzles

Oh... I knew there must be some hocus-pocus I was not privy to. Thank you for mentioning that