Let x = y

x + x = y + x

2x = y + x

2x - 2y = y + x - 2y

2 (x - y) = x - y

2 = (x - y) / (x - y)

2 = 1

:D :naughty:

division by zero :D

ibalik ko..... ina ya ang TUPVian!... narecall pa ang good old school! :thumb: :thumb: :thumb:

Amo na ya! This is one wrong application of the multiplication property of equality. If we multiply zero to both sides of the equation, both sides will always end up as zero, thus defeating the real values of the expressions in the equation. But what if we just operate with zeroes lang?


0 / 1 = ?

1 / 0 = ?

0 / 0 = ?

Back to old school gid ni.

0/1 = 0

1/0 = infinity

0/0 = ??? .... infinity cguro :lol:

Let's dissect one by one:

0 / 1 - how many ones can you get out of a zero? so the practically, we can get no ones out of a zero so the answer is none

1 / 0 - how many zeroes can you get out of a one? the answer is limitless because no matter how many zeroes we get, we still have 1 remaining. so "infinity" is right

0 / 0 - how many zeroes can we get out of a zero. Since we are counting zeroes, the impression is that there is an infinite number of zeroes as well. But since we started with zero to begin with, there is now a confusion as to where we should start counting and where do we need to end. So the logical answer is "undefined"


From our original discussion above, the term (x - y) / (x - y) then is actually "undefined"

damu ko bala nakilala nga nursing, med tech kag chemical eng's hotties tungod sang algebra kag trigo........ :lol: :lol: :lol: :lol:

ara na naggwa na ang abilidad, indi na ina diri pag dal-a kay tutorial section ina diri...

:angry: :woot:

narecall ko lang ah.... sensya meg :OT ako :lol: :lol: :lol: :lol:

hehehe! Sobra gid ya ka maabilidad mo! :P :P



Pamangkot para sa tanan.

When was the first time you encountered Algebra. Try to remember... *:shrug:

unahan ko sabat....i was in grade 5..... that was before the time that i felt in love with mathematics..... :thumb: :thumb: :thumb:

may lower pa?

arithmetic na guro kung may lower pa... . :lol: :lol: :lol: :thumb:

:thumb: :thumb: :thumb:

I think, I remember grade 2.

Do you remember...

8 + __ = 11

then you need to find the __. This is algebra already. Galing kay sang gin-islan na X ang __, indi na kabalo ang mga bata!


Believe it or not, my kids already get this lesson from kinder school! HuWow!

hehehe..... insakto gid....

nagakadlaw ko kay amu ini ang lesson sang Jr Kinder ko last school year.....

(+) times (+) = + ok
(-) times (+) = - ok
(-) times (-) = + why, bakit, nga-a????? *no *no

Let's understand these concepts in the real world scenario. Let us take (-) as "utang". So...

(+) * (+) = (+), no issue

(-) * (+) = (-), ang utang, ginpadamo sang pila ka beses, nagdako ang utang

(-) * (-) = (+), ang utang, ginpaaliwasan pila ka beses, kundi nadula ang utang

Daw kagamo?

(-) / (-) = (+), ang utang, tungaon sa tagpila nga utang, ang sabat kundi positibo nga numero.

Halimbawa:

-10 / 5 = -2, ang utang nga pulo, tungaon sa lima. Kundi tig duwa... nga utang.

-10 / -5 = 2, pila ka tig lima nga utang ang ara sa utang nga pulo? Ti, kundi duwa.

Etymology

The word Algebra is derived from the Arabic word Al-Jabr, and this comes from the treatise written in 820 by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī entitled, in Arabic, كتاب الجبر والمقابلة, or al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, which can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. Although no one knows with absolute certainty what the word al-jabr means, most historians agree that the word meant something like "restoration" or "completion".[1]



Stages of algebra

Rhetorical algebra, where equations are written in full sentences. For example, the rhetorical form of x + 1 = 2 is "The thing plus one equals two" or possibly "The thing plus 1 equals 2". Rhetorical algebra was first developed by the ancient Babylonians and remained dominant up to the 16th century.

Syncopated algebra, where some symbolism is used but which does contain all of the characteristic of symbolic algebra. For instance, there may be a restriction that subtraction may be used only once within one side of an equation, which is not the case with symbolic algebra. Syncopated algebra was first developed by Diophantus in his Arithmetica and then later in the Bakhshali Manuscript.

Symbolic algebra, where full symbolism is used. Symbolic algebra sees its culmination in the work of Leibniz.

i-derive man ang quadratic equation.

Mayo gid mag isplikar si manong Raymie ah. More Q & A please. Daw kanami gali magbasa kun Ilonggo ang tutorial noh. :bounce

before goidn through... one must review his binomial process of solving quadratic equation and factoring....(binomial is a reverse of factoring actually)

here if goes:

Ax^2 + Bx + c = 0

dividing by A

x^2 + B/A X + C/A = 0

transferring C/A

X^2 + B/A x = -C/A

using binomial formula --> one must recall this....

X^2 + B/Ax + (B/2A)^2 = -C/A + (B/2A)^2

simplification by factoring

(X+b/2a)^2 = (b/2a)^2 - c/a = (b^2 - 4ac)/2a

by square root

X + b/2a = sqrt( b^2 -4ac)]/2a

transferring


x =[-b +/- sqrt(b^2 -4ac] / 2a

Why do we have to start with equating everything to zero?

simplification.... :thumb:

Why not simplify it to any other number? For example:


X^2 + 2X + 10 = 0 vs X^2 + 2X = -10

Still the same supposed to be.

depende sa process na in undergo guro... kung "completing the square" ti indi dapat zero ang pihak nga side sang equation pero kung usaran quadratic formula, zero ang pihak nga bahin sang equation para makuha ang factor...

well... cguro.. wahehehehehe

You are nearing the light! You mentioned "factor". So ngaa zero uli? hint: factor :P

ti kay para exact ang factor kung zero ang sa pihak nga side... indi ko lang guro makuha ang accurate word nga gusto mo wahehehehhe

Buligan ta si Toto Rostan. Diri na ankla ang bilog ta nga proseso mag solve sang any algebraic equation. :D

Ilisan ko ang guide question para daw mas klaro.

In many algebraic equations, ngaa gina-equate naton sa zero para ma-solve naton ang variable? Normally, we don't do that for linear equations. Pero pag may exponents na, we would equate it to zero to get the root(s). Again, ngaa? :unsure:

one reason maybe kung may exponents na, meaning may certain characteristics na ina sya....

as far as i know, we are equating it to zero to at least determine kung anu ang iya characteristics... may it be circle, parabolo, hyperbola, uneven curve or a wave.....

Ang isa ka algebraic equation gina-equate naton sa zero kung ginsuspetsuhan ta nga pwede sya i-reduce to two or more "factors". Ngaa liwat. Because...

Kung ang equation in one variable can be reduced to the form:

A * B = 0

then we can conclude that either A = 0 or B = 0 or that both are equal to zero. (remember, any number multiplied to zero results to zero).

Example:

X^2 + 2X = 8

We would be having a hard time finding the value of X that would result to 8. However, we can do better by:

X^2 + 2X - 8 = 0 (by addition property of equality)

then we factor into:

(X + 4)(X - 2) = 0 which then gets the form of A * B = 0 as above

Based on our previous argument, A and B can be equal to zero, thus making the equation valid, thus:

X + 4 = 0 and therefore reducing to X = -4

and:

X - 2 = 0, reducing to X = 2

So, from a higher order equation, we were able to find "factors" equating to zero. Each "factor" being simpler, linear equations when equated to zero which easily gives us the possible root(s) to the original polynomial equation.

Amo ini ang rason ngaa gina-equate naton sa zero para ma solve and mga single variable equations. :thumb: :thumb: :thumb:

:D :thumb: :thumb: :thumb: :thumb:


anu pa gid mayu nga topic sang algebra man?.... :D

ambot gani tan tan ah...

nakapasar lang ko daan sa algebra ko tungod sa converted to 5 nga policy... *ben wallace

4.65 or 4.55? wahehehehe.... indi ko magpati sa imu ya bolitzki!... ikaw pa! :lol: :lol: :lol: :lol:

daw 4.9 man mig ang rounding off?

daw may ara man conditions para dira mig ah... indi ko lang kabisado galing :D

4.7- 1 grade below 6.0
4.8 - 2 grades below 6.0
4.9 automatic 5.0

:thumb: :thumb: :thumb:

Memorize ko na kay 4.7 ko algebra daan sang una :palakan :palakan

hehehehe....... good!.... so masanag ina nga algebra kay puro numero kag conditions :lol: :lol: :lol:

Si Migo Rufin gid he he he he :naughty: :naughty: :naughty:

:thumb: :thumb: :thumb: