Solve. Simplify your answer. Type an exact answer using radicals as needed.
y^2 + 31 = 12y
Solution
y = {8.236067978, 3.763932022}
1. y =(12-√20)/2=6-√ 5 = 3.764
2. y =(12+√20)/2=6+√ 5 = 8.236
Which would be the correct way to answer this equation, the first set, or the numbered set or is this the wrong answer altogether?
y^2 - 12y + 31 = 0
clearly , it does not factor, so let's use the formula
y = (12 ± √20)/2
= (12 ± 2√5)/2
= 6 ± √5
So what do you think?
To solve the equation y^2 + 31 = 12y and simplify your answer, you can use the quadratic formula.
The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -12, and c = -31.
Plugging these values into the formula, we get:
y = (-(-12) ± √((-12)^2 - 4(1)(-31))) / (2(1))
= (12 ± √(144 + 124)) / 2
= (12 ± √268) / 2
Now, you can simplify the answer by writing it in radical form and as a decimal.
1. Simplifying square root of 268:
The square root of 268 is approximately equal to 16.370.
2. Simplifying the expressions:
a) (12 + √268) / 2 = 6 + √67
b) (12 - √268) / 2 = 6 - √67
So, the correct way to express the solutions to the equation y^2 + 31 = 12y is with the second set:
y = {6 + √67, 6 - √67}
In decimal form, these solutions are approximately:
y ≈ {8.236067978, 3.763932022}
Therefore, both the decimal and radical answers are correct, and either form can be used depending on the context or preference.