Olympiad Mathematics | Learn how to solve the system for X, Y and Z quickly | Math Olympiad Training

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Olympiad Mathematics | Learn how to solve the system for X, Y and Z quickly | Math Olympiad Training

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[montynorth]

I multiplied each line by 6.
6/X + 6/Y =
6/Y + 6/Z =
6/X + 6/Z =
I subtracted equation (2) from (3).
6/X + 6/Z - 6/Y - 6 /Z = 1.
Thus 6/X - 6/Y = 1.
I then added this to equation (1).
6/X - 6/Y + 6/X + 6/Y = 4.
12/X =4.
X = 3.
I then substituted in equation (1) to calculate Y, and in equation (3) to calculate Z.

[alster]

Wow, another example of manipulation instead of the traditional solving.

Good job, Premath!

[bigm]

Thanks for another stepwise explanation!🥂❤😀

[theoyanto]

Very interesting manipulation, , my problem is usually knowing where to begin.
thanks again 👍🏻

[HappyFamilyOnline]

Awesome explanation👍👍
Thanks for sharing😊

[krishnaagarwal]

In the given figure, In the given figure, O is the centre of circle passing through A, B, C, D and E. If A overline B = AE BC = CD = DE and 2AB = 3BC then find angle AOB, angle BOC and angle COF .Sir please solve it

[captainkim]

you can also substitute the reciprocated fractions with a b and c respectively.

[misterenter-izrz]

a=1/x, b=1/y, c=1/z, a+b+c=(1/2+2/3+5/6)/2=1, x=1/(1-2/3)=3, y=1/(1-5/6)=6, z=1/(1-1/2)=2, done.😊

[devondevon]

Answer 3, 6, and 2
2/x + 2/y + 2/z = 2/3 + 5/6 + 1/2 add all three equations
2(1/x + 1/y + 1/z= 2 factor out 2
1/x + 1/y + 1/z=1 divide both sides by 2
1/2 + 1/z = 1 substitute the value for 1/x + 1/y
1/z = 1/2
1/y + 5/6 =1 substitute the value for 1/x + 1/z
1/y = 1/6
1/x + 2/3 = 1
1/x =1/3
Since 1/x =1/3, 1/y =1/6 and 1/z =1/2 then
x =3 , y = 6 and z =2

[LearningAcademy-jpgg]

Sir just put the value of of 1/y or 1/z or 1/x in any equation and then it's value gets easily calculated

[sadafkhanam]

2(1/x+1/y+1/z)= 1/2+2/3+5/6
1/x+1/y+1/z= 1
Now,
1/z= 1-1/2
Z= 2
1/y=1-5/6
Y=6
1/x= 1-2/3
x=3
So,
x=3, y=6, z=2 ans..😊😊

[guidichris]

Slightly different approach. Substitute a=1/x, b=1/y, c=1/z. End up with a=1/3, b=1/6, c=1/2.

[musicsubicandcebu]

Find 1/x in terms of y
Find 1/z in terms of y
Substitute in equation 3 and solve for y . . . etc.

[neverythingk]

One different approach
Subtract equation 2 in equation 1
And then add that to equation 3 and now you get x .
Similarly find y and z

[sakshamkumar]

eq1-eq2-eq3
Result z=2
Put z in 3
x=3
Put x in 1
y=6

[ckjain_maths]

Is it unique solution? The solution is incomplete without proving that it is unique solution. Does The set of equation not have any other real or imaginary solution.?

[Denish_Uprety]

25) If sqrt(x - 3a) + sqrt(x - 3b) = sqrt(x - 3c) then prove that x = (a + b + c) plus/minus 2 * sqrt(a ^ 2 + b ^ 2 + c ^ 2 - ab - bc - ca)

[amritanshuprusty]

I have sent my questions in your email. Please solve my queries

[Denish_Uprety]

Please solve tommorow is my exam25) If sqrt(x - 3a) + sqrt(x - 3b) = sqrt(x - 3c) then prove that x = (a + b + c) plus/minus 2 * sqrt(a ^ 2 + b ^ 2 + c ^ 2 - ab - bc - ca)