What is the general solution for 4sinh(x^3)=0 ?

The general solution for 4sinh(x^3)=0 is x=0

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Popular >

4sinh(x^3)=0

Solution

4 sinh (x^{3}) = 0

Solution

x = 0

Degrees

x = 0^{\circ}

Solution steps

4 sinh (x^{3}) = 0

Rewrite using trig identities

4 sinh (x^{3}) = 0

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

4 \cdot \frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0

4 \cdot \frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0

4 \cdot \frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0 : x = 0

4 \cdot \frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

\frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0

Solve

\frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0 : x = 0

\frac{e ^{x^{3}} - e ^{- x^{3}}}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

e^{x^{3}} - e^{- x^{3}} = 0

Add

e^{- x^{3}}

to both sides

e^{x^{3}} - e^{- x^{3}} + e^{- x^{3}} = 0 + e^{- x^{3}}

Simplify

e^{x^{3}} = e^{- x^{3}}

Apply exponent rules

e^{x^{3}} = e^{- x^{3}}

a^{f (x)} = a^{g (x)}

, then

f (x) = g (x)

x^{3} = - x^{3}

x^{3} = - x^{3}

Solve

x^{3} = - x^{3} : x = 0

x^{3} = - x^{3}

Move

x^{3}

to the left side

x^{3} = - x^{3}

Add

x^{3}

to both sides

x^{3} + x^{3} = - x^{3} + x^{3}

Simplify

2 x^{3} = 0

2 x^{3} = 0

Divide both sides by

2

2 x^{3} = 0

Divide both sides by

2

2 x^{3} = 0

Divide both sides by

2

\frac{2 x ^{3}}{2} = \frac{0}{2}

Simplify

x^{3} = 0

x^{3} = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

x = 0

x = 0

x = 0

x = 0

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 4sinh(x^3)=0 ?
The general solution for 4sinh(x^3)=0 is x=0