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aleksandr82 [10.1K]
3 years ago
7

Answer with steps by step please ​

Mathematics
1 answer:
suter [353]3 years ago
7 0

Answer:

a is 1

Step-by-step explanation:

a+\dfrac{1}{a}=2

Multiply both sides by a:

a^2+1=2a

Move everything to one side:

a^2-2a+1=0

Factor:

(a-1)^2=0

By the zero product rule, a is 1.

Therefore, the expression is true, because:

(1)^2+\dfrac{1}{a^2}=a^4+\dfrac{1}{a^4}=1+1=2

Hope this helps!

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