Sissy Devane said:
Give the exact and approximate solutions to three decimal places. I have done problems were the sqaure roots care exact but I am confused with this one.
(x-10)^2=20
There are a couple of ways to approach this problem.
I think the simplest route is to take the square root of both sides of the equation:
sqrt[ (x - 10)[sup:8i5ee1c8]2[/sup:8i5ee1c8] ] =
+ sqrt(20)
x - 10 =
+ sqrt(20)
You can simplify sqrt(20) since 20 has a factor of 4. sqrt(20) = sqrt(4*5) = 2 * sqrt(5)
So,
x - 10 =
+ 2*sqrt(5)
Add 10 to both sides, and you get
x = 10
+ 2*sqrt(5)
These are the
exact answers: 10 + 2*sqrt(5) and 10 - 2*sqrt(5)
For the approximate decimal answers, use your calculator to get the approximate value of sqrt(5), and then, following the order of operations, do the arithmetic.
As an alternative, you could
expand (x - 10)[sup:8i5ee1c8]2[/sup:8i5ee1c8]:
(x - 10)[sup:8i5ee1c8]2[/sup:8i5ee1c8] = x[sup:8i5ee1c8]2[/sup:8i5ee1c8] - 20x + 100
And your equation becomes
x[sup:8i5ee1c8]2[/sup:8i5ee1c8] - 20x + 100 = 20
Subtract 20 from both sides, so that the right side is 0:
x[sup:8i5ee1c8]2[/sup:8i5ee1c8] - 20x + 80 = 0
Apply the quadratic formula, with a = 1, b = -20, and c = 80. You should get the same solutions.
