Answer:
The key to verbal problem is to translate the words into a mathematical expression.
"Eight more then the square of a number": the number is unknown thus it is "x". The square of the number is x^2.
Eight more is 8+x^2.
So 8+ x^2 "is the same as six times the number". Our number is "x" and six times of the number is 6x.
Therefore our equation is: 8 + x^2 = 6x
Subtracting 6x from both sides of the equation is: 8 + x^2 - 6x = 0
Rearranging it x^2 - 6x + 8 =0
This can be solved by the quadratic equation: ( -b +- (b^2 - 4ac)1/2)/ 2a for ax^2 + bx + c =0
(6+-(6*6 - 4*1*8)1/2/2*1
(6+-(36-32)1/2)/2
(6+-(4)1/2)/2
The two solutions are:
(6+2)/2 and (6-2)/2
4 and 2
Alternatively one can recognize that the equation x^2 - 6x + 8 = (x-4)(x-2) = 0 so x = 4 or x = 2
Therefore there are two numbers that satisfies this question 4 and 2.
Step-by-step explanation:
Hope it helps pa brainliest nga po pala
