Answer:
x = 2 ±sqrt( 97)
Step-by-step explanation:
log10(x^2 -4x+7) =2
Raise each side to the base 10
10 ^ log10(x^2 -4x+7) =10^2
x^2 -4x +7 = 100
Subtract 7 from each side
x^2 -4x+7-7 = 100-7
x^2 -4x = 93
Complete the square
-4/2 = -2 (-2)^2 = 4
Add 4 to each side
x^2 -4x+4 = 93+4
(x-2)^2 = 97
Take the square root of each side
sqrt((x-2)^2 )=±sqrt( 97)
x-2 = ±sqrt( 97)
Add 2 to each side
x = 2 ±sqrt( 97)
The roots of f(x) are the values for x at which f(x)=zero. The root of f(x) at point P is a bit redundant, since point P is the root of the function (and based on the graph, the only root).
We could plug zero in for f(x) to find the value of x at Point P, but based on the graph/options provided and the complexity of the function, it may be easier to just eyeball the graph to get the correct answer. We see that point P is between 1/2 and 1 on the x-axis.
Of the options provided, we want the value for x that satisfies: 1/2 < x < 1
a) 1/2 < 3/5 < 1 CORRECT ANSWER
b) 1/5 < 1/2 INCORRECT
c) 5/3 > 1 INCORRECT
d) 1/3 < 1/2 INCORRECT
so 難しいポイントが必要です
Step-by-step explanation:
さようなら.