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Nairaland Forum / Nairaland / General / Education / Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. (2203 Views)
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Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 8:36am On Mar 04, 2017 |
Pls guys, I've attached the question. I did it to a point and got my value of xyz to be 15. I just can't get the numbers themselves.
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Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by RealLordZeus(m): 8:42am On Mar 04, 2017 |
Not this morning... Run out of thread |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by Nobody: 8:56am On Mar 04, 2017 |
X+y+z=1.....(1)
X^2+y^2+z^2=35......(2)
X^3+y^3+z^3=97.......(3)
From equ(3)
We that x^3+y^3=(x+y)^3-3xy(x+y)
So input that into equation(3)
(x+y)^3-3xy(x+y)+z^3=97....(4)
Using equ(1) x+y=1-z....(5)
Subt into equ(4)
(1-z)^3-3xy(1-z)+z^3=97
1-3z+3z^2-z^3-3xy(1-z)+z^3=97
Collect like terms
-3z+3z^2-3xy(1-z)=96......(6)
From equ(2)
x^2+y^2=35-z^2....(7)
Also x^2+y^2=(x+y)^2-2xy.....(
But x+y=1-z so
x^2+y^2=(1-z)^2-2xy....(9)
Equate equ(7) to equ(9)
35-z^2=(1-z)^2-2xy
Make xy the subject and subt into equ(6)
xy=z^2-z-17
Put it into -3z+3z^2-3xy(1-z)=96
-3z+3z^2-3(z^2-z-17)(1-z)=96
Divide through by 3 andExpand the bracket and
collect like terms
z^3-z^2-17z-15=0
Solve the polynomial
z=-1, z=-3 z=5
Subt for x and y in each value of z
x=-1, x=-3 x=5
And y=-1, y=-3, y=5. 2 Likes |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 8:56am On Mar 04, 2017 |
RealLordZeus:haha. Abeg help bro. It's not compulsory you must solve it in the morning. You can solve it in the afternoon. |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 8:58am On Mar 04, 2017 |
mikezuruki:. Thanks very much bro. I'm very grateful. |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by nextprince: 9:04am On Mar 04, 2017 |
X=5 Y= -3 Z= -1 1 Like |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 9:12am On Mar 04, 2017 |
nextprince:Thanks very much bro. . |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by nextprince: 9:26am On Mar 04, 2017 |
sureteeboy: In this equation, there is no unique value attached to any of the unknowns. They are interchangeable. Attempt interchanging the values I stated and check, u will arrive at the same answer. Eg 5-3-1=1 -3+5-1=1 -1-3+5=1 Or 5^2-3^2-1^2=35 -3^2+5^2-1^2=35 -1^2-3^2+5^2=35 Same with the third equation. Such elaborate working ain't necessary especially when time is a factor. From equation 1, it is very apparent that there are negative and positive values And from equation 2, the square of any number is positive and certainly non of the numbers should be more than 6. Therefore, u can choose from -4 to 5 and be adding the squares of different combinations. I got it at equation 2, and simply confirm it with equation 3. 1 Like |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 10:28am On Mar 04, 2017 |
nextprince:Thanks Bro. I figured that out, that's why I deleted the question. I never knew you saw it. 1 Like |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by dejt4u(m): 10:55am On Mar 04, 2017 |
(x, y, z) = (-1, -3, 5) OR (x, y, z) = (-3, 5, -1) OR (x, y, z) = (5, -1, -3) |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 2:33pm On Mar 04, 2017 |
mikezuruki:Pls Bro, I solved the polynomial but I don't understand what you meamt by ;substitute for x and y in each value of z. |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by Nobody: 3:47pm On Mar 04, 2017 |
sureteeboy:If you've gotten the unknown(s) for x and y, no need solving for z. Just subtitute the figures gotten for both x and y |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 3:52pm On Mar 04, 2017 |
mikezuruki:No, what I meant was, I solved the polynomial and I got the 3 values of z. Now, how do I get the values of x and y from there? |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 7:27am On Mar 05, 2017 |
mikezuruki:Bro please, kindly assist for this last time. After getting those values of z, I don't know where to substitute them to get each values of x and y |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by Tellemall: 6:20am On Mar 06, 2017 |
sureteeboy: Then find x or y the same way you found z. You only need to know two of the unknowns to solve for x, y [/i]and [i]z. |
Re: Pls, Mathematicians, Kindly Help Me Solve This System Of Equations. by sureteeboy(m): 2:28pm On Mar 06, 2017 |
Tellemall:Yeah. I've already done it. Thanks very much. |
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