What is the answer to sqrt(2y^2+1)= 6/y ?

The answer to sqrt(2y^2+1)= 6/y is y=2

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sqrt(2y^2+1)= 6/y

2 y^{2} + 1 = \frac{6}{y}

y = 2

Solution steps

2 y^{2} + 1 = \frac{6}{y}

Multiply both sides by

y

2 y^{2} + 1 y = \frac{6}{y} y

Simplify

2 y^{2} + 1 y = 6

Square both sides:

2 y^{4} + y^{2} = 36

2 y^{4} + y^{2} = 36

Solve

2 y^{4} + y^{2} = 36 : y = 2, y = - 2

y = 2, y = - 2

Verify Solutions:

y = 2

True

, y = - 2

False

The solution is

y = 2

2 x + 8 = 6

2 x + 8 = 5

2 x + 5 + 4 = x

x^{2} - 2 3 x + 4 = 0

What is the answer to sqrt(2y^2+1)= 6/y ?
The answer to sqrt(2y^2+1)= 6/y is y=2
Solve for y: sqrt(2y^2+1)= 6/y
The solution is y=2