What is the answer to y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y ?

The answer to y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y is y=(1.41421…+sqrt(7))/2 ,y=(1.41421…-sqrt(7))/2

Solve for y: y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y

The solution is y=(1.41421…+sqrt(7))/2 ,y=(1.41421…-sqrt(7))/2

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y = 2 ∣ 0.5 ∣ + \frac{- ∣ 0.5 ∣ - 0. 5 ^{2} + 2}{y}

y = \frac{1.41421 \dots + 7}{2}, y = \frac{1.41421 \dots - 7}{2}

Decimal Notation

y = 2.02998 \dots, y = - 0.61576 \dots

Solution steps

y = 2 ∣ 0.5 ∣ + \frac{- ∣ 0.5 ∣ - 0. 5 ^{2} + 2}{y}

Simplify

\frac{- ∣ 0.5 ∣ - 0. 5 ^{2} + 2}{y} : \frac{1.25}{y}

y = 2 ∣ 0.5 ∣ + \frac{1.25}{y}

Multiply both sides by

y

y^{2} = 2 0.5 y + 1.25

Solve

y^{2} = 2 0.5 y + 1.25 : y = \frac{1.41421 \dots + 7}{2}, y = \frac{1.41421 \dots - 7}{2}

y = \frac{1.41421 \dots + 7}{2}, y = \frac{1.41421 \dots - 7}{2}

Verify Solutions

Find undefined (singularity) points:

y = 0

Combine undefined points with solutions:

y = \frac{1.41421 \dots + 7}{2}, y = \frac{1.41421 \dots - 7}{2}

6 d - 3 (7 d - 1) \geq - 3 d - 6 (2 d - 1)

x^{2} + 8 x - 1 = 0

4 x - 14 = x - 1 + x + 7

\frac{1}{2 ^{1}}

\frac{6 a ^{2} + 21 a}{3 a ^{2}}

What is the answer to y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y ?
The answer to y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y is y=(1.41421…+sqrt(7))/2 ,y=(1.41421…-sqrt(7))/2
Solve for y: y=2sqrt(|0.5|)+(-|0.5|-0.5^2+2)/y
The solution is y=(1.41421…+sqrt(7))/2 ,y=(1.41421…-sqrt(7))/2