solve for y: the square root of 3y plus 4 plus the square root of 5y plus 6 equals 2

sqrt (3y+4) + sqrt (5y+6) = 2

Squaring both sides, [sqrt (3y+4) + sqrt (5y+6)]^2 = 2^2

3y+4 +5y+6+ 2 sqrt [(3y+4) (5y+6)] = 4

8y+10 +2 sqrt (15y^2 + 38y + 24) =4

2 sqrt (15y^2 + 38y + 24) = 4 -8y-10

2 sqrt (15y^2 + 38y + 24) = -8y-6

sqrt (15y^2 + 38y + 24) = -4y-3

sqrt (15y^2 + 38y + 24) = - (4y+3)

Squaring both sides, 15y^2 + 38y + 24 = ([ - (4y+3)]^2

15y^2 + 38y + 24 = 16y^2 + 24y + 9

y^2 - 14y - 15 = 0

(y-15) (y+1) = 0

or y = 15, -1

Since y =15 cannot satisfy the orginal equation,

the solution is y = -1

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