A Cute Question From The Brazilian Math Olympiads

since x=6 is given hence substituting this in the equation gives us 2(6*6) - A(6) + 60 =0. Hence A = wiped out number = 22

Set the erased number as y and x =6: 72 - 6y + 60 = 0 ; y = ( 72 + 60 ) / 6 ; y = 22

We must use the concept of producr of roots tat is c/a and sum of roots tat is -b/a

Set the unknown coefficient as a then plug in the value of 6 for x and then solve: $2(6^2)-a(6)+60=0$ $72-6a+60=0$ $6a=72+60$ $a=\frac{132}{6}$ $a=22$

the first solution is x=6, the seconde must be x=5 to have 2 6 5=60 2(x-6)(x-5)=2( x²-5x-6x+30)=2x²-22x-60

2(6^2)-6y+60=0 so 6y=132 and y=22

let C be the value of the coefficient of x then substitute the value of x=6 6C=2(6*6)+60 C=22

take the coefficient to be k and substitute x=6 so we obtain 72-k6+60=0 or 132-k6=0 or k6=132 or k=132/6 = 22

Just represent the coefficient of x with any variable then substitute all x's with 6, then simplify to get 22.

In the chalkboard we can see that one of the root of the equation is 6. So, we can subtitute one of the root to get the answer, 2(6*6)-a(6)+60=0.--> 72+60=6a.--> a=22. Finish.

By letting 2x^2 - ax + 60 = 0,

as one of the 2 roots is 6,

2(6)^2 - 6a + 60 = 0 ,

72 + 60 = 6a

a = 132 / 6 = 22,

therefore a=22 ,would be 2x^2 - 22x + 60,

For x = 6 then the initial equation that is 2x ^ 2-ax +60 = 2 (6) ^ 2-a (6) +60=72-6a +60= 132-6a = 0 so obtained a = (-132) / (-6) = 22

let the product value is 120. so we can solve it by (12*10)=120. hence the sum of (12 and 10) will be the answer.

2(6*6) - 6y+60=0 so 6y =132 and y=22

Root X = 6; (x-6) , (2x-n); x=n/2, then 6n = 60