Question

Solve `sqrt(y + 1) + sqrt(2y - 5)` = 3

Answer 1

`sqrt(y + 1) + sqrt(2y - 5)` = 3           ...(squaring on both sides)

`(sqrt(y + 1) + sqrt(2y - 5))^2` = 3² 

`(sqrt(y + 1))^2 + (sqrt(2y - 5))^2 + 2(sqrt(y + 1))(sqrt(2y - 5))` = 9

`y + 1 + 2y - 5 + 2 sqrt((y + 1)(2y - 5))` = 9

`3y - 4 + 2 sqrt(2y^2 - 5y + 2y - 5)` = 9

`2sqrt(2y^2 - 3y - 5)` = 9 + 4 – 3y

= 13 – 3y                  ...(squaring on both sides)

`[2sqrt(2y^2 - 3y - 5)]^2` = (13 – 3y)²

4(2y² – 3y – 5) = 169 + 9y² – 78y

8y² – 12y – 20 = 169 + 9y² – 78y

8y² – 9y² – 12y + 78y – 20 – 169 = 0

–y² – 66y – 189 = 0

y² – 66y + 189 = 0

(y – 3) (y – 63) = 0

y = 3 or y = 63

The value of y is 3 and 63.