Question

if a= root 2 + 1/root 2 -1 and b = 1/a find the value of a²+b²








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Answer 1

Answer:

$\small\red{Here \: is \: your \: answer}$

Step-by-step explanation:

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

$\frac{ \sqrt[2]{2} + 2 \times \sqrt{2} \times 1 + {1}^{2}}{\sqrt[2]{2} - {1}^{2} }$

$\frac{2 + 1 + 2 \sqrt{2} }{3}$

$\frac{3 + 2 \sqrt{2} }{3}$

$= 2 \sqrt{2}$

$b = \frac{1}{a}$

$\frac{1}{b} = \frac{1}{a}{a}$

$\frac{1}{a} = \frac{a}{a} = a$

∴

$∴ {a}^{2}+{b}^{2} </p><h2></h2><h2>$

$= > 2 \sqrt{2 } + a$