A Nice Algebra Problem

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Жыл бұрын

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Пікірлер: 76

@pavelgatnar7164 Жыл бұрын

From x+y+1=0 we get -y=x+1. Substitution to x^2-y=73 gives x^2+x+1=73. This gives x^2+x-72=0. This can be factored as (x+9)*(x-8) =0. So the solutions are [-9, 8] and [8, -9]

@user-fb3gs5vh4l Жыл бұрын

빠른 정답입니다

@TheDerlick 11 ай бұрын

This is the way to solve this problem, 100%. I felt resolution in the problem but then it started getting way more complicated. Your method is exactly how I solved this problem. Took around 1 minute. I've seen so many problems by this guy where things start out good but then take crazy directions. My theory is he doing it on purpose to make us comment...

@joeaberman449 9 ай бұрын

in a square you have 4 corners a b c d you can go from a to b or you can go from a to d to c to b how would you rather do it? you could have solved the problem after equation 3 by substitution or if you have to lose weight you can walk the long way

@miyachan7625 Жыл бұрын

(x,y)=(8,-9),(-9,8) 根号を外したときに ±（x-y）=17 とすべき。

@briannordin Жыл бұрын

Fun problem and fun solution! At 8:33 there's a small issue. When you take the square root of 289 there are 2 possible answers: +17 and -17.

@shmuelzehavi4940 10 ай бұрын

That's right, and based on the fact that the original SOE is symetric in x , y he could solve for the case: x > y only and get the second solution by interchanging values between x and y. He should mention this.

@joeaberman449 9 ай бұрын

@@shmuelzehavi4940 in a square you have 4 corners a b c d you can go from a to b or you can go from a to d to c to b how would you rather do it? you could have solved the problem after equation 3 by substitution or if you have to lose weight you can walk the long way

@alexkushnir5331 Жыл бұрын

you missed the solution: (x-y)=+17 and (x-y)=-17. That leads to two pairs of solution: 1) x=8, y=-9 and 2) x= -9, y=8

@mohammedel-aminelahcene1344 Жыл бұрын

at 8:28 , there are two solutions x-y or -(x-y)

@TheDerlick 11 ай бұрын

@mohammedel-aminelahcene1344 he said x-y = 17 however x-y = +/- 17. He missed this point.

@ahmethulisiarslan8829 10 ай бұрын

You missed there is two solution

@matthewmcdaid7962 Жыл бұрын

The squares nearest 73 are 64 and 81. By inspection, it is evident that 64 +9 =73 and 81 - 8 = 73, thus x = -9 and y = 8 satisfies the conditions.

@awful7436 Жыл бұрын

When we get the conclusion x+y+1=0 ( x=-(y+1) ), we can get a equation: (-(y+1))**2 -y = 73. This method is more easier.

@DrCarter33 Жыл бұрын

Exactly

@Kat-dp4rh Жыл бұрын

But since the equations are symmetrical, it also works with x = -9 and y = 8

@youngbear9945 Жыл бұрын

I agree. The equ. also works with (x,y)=(-9, 8).

@rengarajramgovind5910 Жыл бұрын

@@youngbear9945Sq rt of 289= + or - 17

@jeffreycharlton335 Жыл бұрын

The square root of 289 can be 17 or -17 hence the X and Y value being interchangeable

@giovannimaccarrone9209 Жыл бұрын

Too long and not all solutions have been found.

@kondalaraon174 8 ай бұрын

Nice explanation

@learncommunolizer 8 ай бұрын

Thanks and welcome🙏❤️🙏

@samarpalsingh6222 10 ай бұрын

Good explanation Thank you

@sundaramsadagopan7795 Жыл бұрын

Simple problem solved with long steps to keep the telecast duration also long. Godd idea.!!

@kimba381 Жыл бұрын

No, no, no. Once you have x+y+1 =0 write y = -x-1, sub into (1) and solve the quadratic. done. This produces x = -9 and 8. By symmetry (x,y) = (-9,8) or (8,-9) If you prefer, sub x= -9 and x = 8 into (1) for the same solution. You only did half the job,.

@user-ly6xg3uo9h Жыл бұрын

Where does the condition "x NE y" come from? You missed another pair of solutions: x=y=(1+/-sqrt(293))/2

@indomath70 Жыл бұрын

It's a conclusion for case (x^n +(x+1)^n) and 2x^n. RHS will always larger for x > 1 and n > 1. Please check it

@pasqualeiw0hex95 Жыл бұрын

Root squadre 289 is +/- 17 so we have 2 simmetrical solutions; you are missing -17 solutions ! Regards !

@acnmes 6 ай бұрын

xy=-72 et x+y=-1 soit y=-x-1 D'ou -x(x+1)=-72 x²+x-72=0 On fait delta et tout le toutim et c'est bon. Pas besoin de se compliqué la tache à recalculé des equation intermediaire

@ssalmero Жыл бұрын

Also making x**2-y=y**2-x, then x**2-y**2= y-x, factirizing x+y you get x+y=-1 and the solution is trivial

@robertmccully2792 Жыл бұрын

For me it's always easer if X & Y have a real named argument/name . Like y = 2 corvettes & X is speed. Which in that case i would call it C for corvette & S for speed.

@tarielmikeladze Жыл бұрын

A) X=-9 Y=8 B) X=8 Y=-9

@manojkantsamal4945 6 ай бұрын

Nice, y= -9 &x= 8

@sj7f Жыл бұрын

x2-y=73=y2-x, x2+x=y2+y, so x=y, x2-x=73, x =1/2(1+-sqrt(01+4*73))

@joeaberman449 9 ай бұрын

@daddykhalil909 Жыл бұрын

When you extracted the sort of 289 why did you ignore the negative root??

@bckitz Жыл бұрын

This is for about 10 lines, not 10 pages... What for you do this?

@davidbrisbane7206 Жыл бұрын

x² - y = 73 & y² - x = 73 So, x = y² - 73, as y² - x = 73 so, (y² - 73)² - y = 73, as x² - y = 73 So, y⁴ - 146y² - y + 5329 = 73 So, y⁴ - 146y² - y + 5256 = 0 So, (y + 9)(y - 8)(y² - y - 73) = 0 So, y = -9, y = 8, y = ½(1 - √293), y = ½(1 + √293). Then x = y² - 73 can be used to solve for y.

@netravelplus Жыл бұрын

Thanks for beautifully explaining.

@learncommunolizer Жыл бұрын

Thanks 🙏❤️🙏

@user-hp9sc8fy9g Жыл бұрын

Very nice.... Thank you !😂

@Fred_DYKim Жыл бұрын

What if x-y = -17?? Please tell us

@LavishDgoat Жыл бұрын

Equations are symmetrical here, he hasn't taken the other case where x-y=-17, if he takes that, it would be x=-9 and y=8 which is also correct.

@shmuelzehavi4940 10 ай бұрын

@@LavishDgoat He forgot to mention this.

@user-qj3sd8of1e 6 ай бұрын

Equate & solve

@zsboya 10 ай бұрын

The x+y = -+17, but since x and y are interchangeable, it is sufficient to carry out only one solution (8, -9).

@salvatorecosta875 6 ай бұрын

I don't understand why you put x≠y if it's not required in the text? For x=y you obtain x=(1±√293)/2 y=(1±√293)/2

@dimitrovniko608 Жыл бұрын

Quite long. But, his explanation is essential to solve exactly. Some people are seemingly bothered, but I'm feeling how important the calculation process is for solution.

@HaNgo-yi9ox 7 ай бұрын

if x is not y then there are two pairs (-9, 8) and (8, -9), we all know both are same but because you want to clarify x is not y :))

@hmed5634 Жыл бұрын

I solved it without writing any thing X+y = -1 Then x squared + X - 72= 0 Then x = - 9 or 8 Then y= 8 or -9

@elainesmallbones2775 Жыл бұрын

What a long way round resulting in only part of the answer.

@rvqx 10 ай бұрын

You missed the second solution because at 8:26 you said: V(x-y)² = x-y , But it also can be: V(x-y)² = - (x-y) and that gives you the other solution.

@NurHadi-qf9kl Жыл бұрын

.x^2-y^2-y-(-x)=0 .(x+y)(x--y)+(x-y)=0 Berarti x=y .x+y=-1 .2x=2y=-1 .x=y=-1/2

@mohamadchouacha2539 Жыл бұрын

What if x+cos(x)=4 how to solve this?

@nicholasngo5428 7 ай бұрын

X=-9, y=8

@Ginkobil50 5 ай бұрын

The equation 5 solution is wrong! It should be x - y = 17 or -(x - y) = 17.

@gwankobejosephbabila8998 Жыл бұрын

But what is the porpoise of

@AleXander__1816 Жыл бұрын

Молодец! Привет из России)

@winmate_longlife Жыл бұрын

X²-Y=8²+9 Y²-X=8²+9 ... ...

@ThaiNguyen-do9vd 9 ай бұрын

Cách giải loanh quanh, nên rất rối.

@elhousseinrattal3158 Жыл бұрын

X^2-y=73. y^2-x=73 => x^2-y -(y^2-x )=73-74=0 => x^2-y^2 +x_y=0 (x-y)(x+y) -(x-y)=0 => (x-y)(x+y-1)=0 => x-y=0 => x=y ou x+y=1 =>2x=1=>x=1/2 et y=1/2

@peteneville698 Жыл бұрын

So tiresome to have a whole extra line written out each time just to add a number or move things to the other side of the equals.

@vishwambharmahant9485 Жыл бұрын

X=8 Y=_9

@robertsullivan9833 Жыл бұрын

rule?

@NurHadi-qf9kl Жыл бұрын

.x^2+y^2-x-y=146 .x(x-1)+y(y-1)=146 & x^2-y^2-x+y=0 .x(x-1)-y(y-1)=0 .2x(x-1)=146; x^2-x-73=0 .x={1+_¥(293)}/2 .73-y^2+y=0; y^2-y+73=0, y imaginer

@arifbudiono158 Жыл бұрын

From x+y=-1 and x.y=72 you can easy solution x=-9 and y=8 or x=8 and y=-9

@pierregakwandi9005 11 ай бұрын

xy=-72

@customarylover3857 6 ай бұрын

Answer: x = -9, y = 8

@kaushikbasu9707 Жыл бұрын

minus 9 and 8 and 8 and minus 9

@JimmyBaevsky 10 ай бұрын

(x-y)(x+y)+x-y=0 (x-y)(x+y+1)=0 x+y=-1 x=-y-1 (-y-1)^2-y=73. y^2+y-72=0 y=-1/2+-rt2(1/4+72)=-0.5+-17/2 y1=-8 y2=--9 x1=-9 x2=8😂

@ermirabrasha6564 Жыл бұрын

You lost one solution. I solved it like you to the point where x+y=-1. Instead, I expressed y=(--x-1) and replaced the value in equation (1) X^2-(-x-1)=73 X^2 + x +1 =73 X^2-+x-72=0 Solutions for this quadratic equation are: x=-9 and x=8 Find y for these X values and we get 2-solutions for the system of equations: (-9, 4) and (8, -9)