MATH SOLVE

2 months ago

Q:
# [tex] \sqrt[3]{ \sqrt[3]{2} - 1} = \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{ \frac{1}{9} } \\ \\ If \: a>b \: \: , \: \: Find \: \: (a+2b) \:.[/tex]

Accepted Solution

A:

Step One

Subtract cube root 1/9 to the left hand side. Or subtract cube root (1/9) from both sides.

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } - \sqrt[3]{ \frac{1}{9} } = \sqrt[3]{a} + \sqrt[3]{b} [/tex]

Step Two.

There is a minus sign in front of [tex] {-}\sqrt[3]{ \frac{1}{9} } [/tex]

We must get rid of it. Because it is a minus in front of a cube root, we can bring it inside the cube root sign like so, and make it a plus out side the cube root sign

[tex] {+}\sqrt[3]{ \frac{-1}{9} } [/tex]

Step Three

Write the Left side with the minus sign placed in the proper place

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } + \sqrt[3]{ \frac{-1}{9} } = \sqrt[3]{a} + \sqrt[3]{b} [/tex]

Step Four

Equate cube root b with cube root (-1/9)

[tex] \sqrt[3]{b} = \sqrt[3]{ \frac{-1}{9} } [/tex]

Step Five

Equate the cube root of a with what's left over on the left

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } = \sqrt[3]{a} [/tex]

Step 6.

I'll just work with b for a moment.

Cube both sides of cube root (b) = cube root (-1/9)

[tex] \sqrt[3]{b} ^{3} =\sqrt[3]{ \frac{-1}{9} }^3} [/tex]

[tex] \text{b =} \frac{-1}{9}[/tex]

[tex] \text{2b =}\frac{-2}{9}[/tex]

Step seven

the other part is done exactly the same way

a = cuberoot(2) - 1.

What you do from here is up to you. It is not pleasant.

Is this clearer?

a + 2b should come to cuberoot(2) - 1 - 2/9

a + 2b should come to cuberoot(2) - 11/9

I hope a person is marking this. I wonder how many of your class mates got it.

Subtract cube root 1/9 to the left hand side. Or subtract cube root (1/9) from both sides.

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } - \sqrt[3]{ \frac{1}{9} } = \sqrt[3]{a} + \sqrt[3]{b} [/tex]

Step Two.

There is a minus sign in front of [tex] {-}\sqrt[3]{ \frac{1}{9} } [/tex]

We must get rid of it. Because it is a minus in front of a cube root, we can bring it inside the cube root sign like so, and make it a plus out side the cube root sign

[tex] {+}\sqrt[3]{ \frac{-1}{9} } [/tex]

Step Three

Write the Left side with the minus sign placed in the proper place

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } + \sqrt[3]{ \frac{-1}{9} } = \sqrt[3]{a} + \sqrt[3]{b} [/tex]

Step Four

Equate cube root b with cube root (-1/9)

[tex] \sqrt[3]{b} = \sqrt[3]{ \frac{-1}{9} } [/tex]

Step Five

Equate the cube root of a with what's left over on the left

[tex] \sqrt[3]{ \sqrt[3]{2} -1 } = \sqrt[3]{a} [/tex]

Step 6.

I'll just work with b for a moment.

Cube both sides of cube root (b) = cube root (-1/9)

[tex] \sqrt[3]{b} ^{3} =\sqrt[3]{ \frac{-1}{9} }^3} [/tex]

[tex] \text{b =} \frac{-1}{9}[/tex]

[tex] \text{2b =}\frac{-2}{9}[/tex]

Step seven

the other part is done exactly the same way

a = cuberoot(2) - 1.

What you do from here is up to you. It is not pleasant.

Is this clearer?

a + 2b should come to cuberoot(2) - 1 - 2/9

a + 2b should come to cuberoot(2) - 11/9

I hope a person is marking this. I wonder how many of your class mates got it.