Don't Be Tricked

Algebra Level 2

It is known that T − 1 T = 5 T-\frac{1}{T}=5

0 < T 0<T

Find ( T + 1 T ) 2 (T+\frac{1}{T})^2


The answer is 29.

Richard Christian by Richard Christian , 20, Indonesia

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1 solution

T − 1 T = 5 ⇒ T 2 + 1 T 2 − 2 = 25 T-\frac{1}{T}=5 \Rightarrow T^2 + \frac{1}{T^2} - 2 = 25

So, T 2 + 1 T 2 = 27 T^2 + \frac{1}{T^2} = 27

Hence, ( T + 1 T ) 2 = T 2 + 1 T 2 + 2 (T+\frac{1}{T})^2 = T^2 + \frac{1}{T^2} + 2

( T + 1 T ) 2 = 27 + 2 = 29 (T+\frac{1}{T})^2 = 27+2 = 29

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I approve this solution, I was about to write it up but since you did it, there's no need to do it again

Ahmed Mouloudi - 6 years, 1 month ago

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