Question

Determine the roots of the following equations: is this an extraneous
√2w+8 / w

Answer 1

To find the roots of this equation, we need to set the expression equal to zero and solve for the variable w.

√2w+8 / w = 0

To eliminate the square root, we square both sides of the equation:

(√2w+8 / w)^2 = 0

Simplifying the left side:

(2w + 8) / w^2 = 0

Now we can solve for w by setting the numerator equal to zero:

2w + 8 = 0

Subtracting 8 from both sides:

2w = -8

Dividing both sides by 2:

w = -4

Therefore, the only root of the equation is w = -4.

However, we need to check if this is an extraneous root. To do this, we substitute w = -4 back into the original equation:

√2(-4) + 8 / -4

Simplifying, we get:

√(-8) + 8 / -4

Since the square root of a negative number (√(-8)) is not a real number, the expression is undefined. Therefore, the root w = -4 is extraneous and the equation has no real roots.