Give the exact and approximatel solutions to three decimal places.
X^2-7x+7=0
use the formula
x = (7 ± √21)/2 ---- > this is exact
or
appr, 5.79 or appr 1.21
oops , you wanted 3 decimals,
5.791 or 1.209
To find the exact solutions to the equation X^2 - 7x + 7 = 0, we can use the quadratic formula:
X = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation to the standard quadratic equation form ax^2 + bx + c = 0, we have a = 1, b = -7, and c = 7.
Substituting these values into the quadratic formula, we get:
X = (-(-7) ± √((-7)^2 - 4(1)(7))) / (2(1))
= (7 ± √(49 - 28)) / 2
= (7 ± √21) / 2
Therefore, the exact solutions are:
X = (7 + √21) / 2
X = (7 - √21) / 2
Now, let's find the approximate solutions to three decimal places.
Using a calculator, we can evaluate the square root of 21, which is approximately 4.58258.
Substituting this value into the equations:
X = (7 + 4.58258) / 2
≈ 11.58258 / 2
≈ 5.79129
X = (7 - 4.58258) / 2
≈ 2.41742 / 2
≈ 1.20871
Therefore, the approximate solutions to three decimal places are:
X ≈ 5.791
X ≈ 1.209