SOLUTION: If a+1/3a=2 then find the value of 9a^2+1/a^2

Question 1206122: If a+1/3a=2 then find the value of 9a^2+1/a^2
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The given equation is .

Square both sides of the equation:

Note that the middle term when squaring the left side of the equation is a constant; it contains no variables. That is the key to solving a problem like this.

Multiply both sides of the equation by 9 to get the expression we want:

ANSWER: 30

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll assume the given equation is
And I'll assume you want to find the value of
Please let me know if otherwise.

If my assumptions are correct, then you should be careful to use parenthesis.
Something like a + 1/3a could be misinterpreted as
So instead of a + 1/3a, you should type in a + 1/(3a)
Instead of 9a^2+1/a^2, you should type in 9a^2+1/(a^2)

The original equation just involves 'a' without any exponent.
The thing we want to find has 'a' being squared.
A naive approach could be to simply square both sides to see what happens.

Use formula (p+q)^2 = p^2+2pq+q^2

The 'a's cancel out in the middle portion.

We want to find , but we have on the left hand side.
The coefficients for the a^2 terms (1 and 9) have been swapped.
A quick easy fix is to multiply both sides by 9.

Answer: 30

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