Chapter 11: Q 6.98 (page 1069)

Solve $16 y^{2} = 32 y^{3} + 2 y$

Short Answer

Expert verified

The value is $y = \frac{1}{4}$

Step by step solution

Given information

Given the equation $16 y^{2} = 32 y^{3} + 2 y$

Bring all terms to one side and solve

Here, we have

$16 y^{2} = 32 y^{3} + 2 y 32 y^{3} + 2 y - 16 y^{2} = 0 32 y^{3} - 16 y^{2} + 2 y = 0 2 y (16 y^{2} - 8 y + 1) = 0$

Use zero factor property and calculate the value

Further solving,

$16 y^{2} - 8 y + 1 = 0 16 y^{2} - 4 y - 4 y + 1 = 0 4 y (4 y - 1) - 1 (4 y - 1) = 0 (4 y - 1) (4 y - 1) = 0 {(4 y - 1)}^{2} = 0 \Rightarrow y = \frac{1}{4}$

Substitute and check the value

Substituting and checking, we get

$16 {(\frac{1}{4})}^{2} = 32 {(\frac{1}{4})}^{3} + 2 (\frac{1}{4}) 1 = \frac{1}{2} + \frac{1}{2} 1 = 1$

So the value is correct

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Solve $16 y^{2} = 32 y^{3} + 2 y$

Short Answer

Step by step solution

Given information

Bring all terms to one side and solve

Use zero factor property and calculate the value

Substitute and check the value

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Solve16y2=32y3+2y

Short Answer

Step by step solution

Given information

Bring all terms to one side and solve

Use zero factor property and calculate the value

Substitute and check the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Decision Maths

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve $16 y^{2} = 32 y^{3} + 2 y$