Question

if a is equal to root 2 + 1 then find the value of a minus one upon a​

Answer 1

Given : expression, $a=\sqrt{2}+1$

To find : The value of $\left(a-\frac{1}{a})$

solution : we have $a=\sqrt{2}+1$

now $\frac{1}{a}=\frac{1}{\sqrt{2}+1}$

⇒$\frac{1}{a}=\frac{1}{\sqrt{2}+1}\times\frac{\sqrt{2}-1}{\sqrt{2}-1}$

⇒$\frac{1}{a}=\frac{\sqrt{2}-1}{(\sqrt{2}+1)(\sqrt{2}-1)}$

⇒$\frac{1}{a}=\frac{\sqrt{2}-1}{(\sqrt{2})^2-(1)^2}$

⇒$\frac{1}{a}=\sqrt{2}-1$

now $a-\frac{1}{a}=(\sqrt{2}+1)-(\sqrt{2}-1)$

= $\sqrt{2}+1-\sqrt{2}+1$

= 2

Therefore $\left(a-\frac{1}{a}\right)=2$

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Answer 2

a- 1/a= 2

Step-by-step explanation:

a=√2-1

1/a=1/√2-1×√2-1/√2-1

= √2-1/(√2)2-(1)2

=