Solve the equation below using completing the square method 6y 2 – y – 15 = 0
Mathematics · High School · Thu Feb 04 2021
Answered on
We have,
6y² - y -15 =0
Dividing both sides by 6
6y²/6 -y/6 -15/6 =0/6
y² -y/6 - 5/2 = 0
It can be written as
(y)² - 2(y)(1/12) + (1/12)² - 361/144 =0
Here, { 1/144 -360/144 = -5/2}
By (a-b)² = a² -2ab + b²
We can write above equation as :
(y - 1/12)² -361/144 =0
(y- 1/12)² =361/144
(y- 1/12) = √361/144
(y- 1/12) = ±19/12
Taking positive value:
(y- 1/12) = 19/12
y = 19/12 + 1/12
y = 20/12
y = 5/3
Taking negative value:
(y- 1/12) =-19/12
y = -19/12 + 1/12
y = (-19+1)/12
y = -18/12
y = -3/2
Thus, value of y are 5/3 and -3/2