Answer:
a. t = 3 + √15 or t = 3 - √15
b. t = 6.87 or t = -0.87
Step-by-step explanation:
a.
Given : t² = 6t + 6
t² = 6t + 6 ⇔ t² - 6t + 6 = 0
USING THE QUADRATIC FORMULA:
[tex]t=\frac{6\pm \sqrt{\left( -6\right)^{2} -4\left( 1\right)(-6) } }{2}[/tex]
Then
[tex]t=\frac{6\pm \sqrt{36 +24 } }{2}[/tex]
Then
[tex]t=\frac{6\pm \sqrt{60 } }{2}[/tex]
Then
[tex]t=\frac{6\pm 2\sqrt{15 } }{2}[/tex]
Then
t = 3 ± √15
Then
t = 3 + √15 or t = 3 - √15
…………………………………………………
b.
t = 3 + √15 = 6.872983346207 ≈ 6.87
or t = 3 - √15 = -0.872983346207 ≈ -0.87
