Question

a+ 1/a = 34 then✓ a +1/✓ a = ?​

Answer 1

Answer:

6

Step-by-step explanation:

Given: a+\dfrac{1}{a}=34

To find: The value of \sqrt{a} +\dfrac{1}{\sqrt{a} }

Now as we know

(a+b)^2 = a^2+b^2+2ab

So we have

(\sqrt{a} +\dfrac{1}{\sqrt{a} })^2=(\sqrt{a} )^2+(\dfrac{1}{\sqrt{a} })^2+2\times\sqrt{a} \times \dfrac{1}{\sqrt{a} }\\\\\Rightarrow (\sqrt{a} +\dfrac{1}{\sqrt{a} })^2= a+\dfrac{1}{a} +2

substitution the value of  a+\dfrac{1}{a}=34

we get

\\\\\Rightarrow (\sqrt{a} +\dfrac{1}{\sqrt{a} } )= 32+2\\\\\Rightarrow  (\sqrt{a} +\dfrac{1}{\sqrt{a} } )=36\\\\\Rightarrow \sqrt{a} +\dfrac{1}{\sqrt{a} } =\sqrt{36} \\\\\Rightarrow \sqrt{a} +\dfrac{1}{\sqrt{a} } =6

Hence ,the value of \sqrt{a} +\dfrac{1}{\sqrt{a} }  is 6

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