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Identity (x+y)(x-y)

If, a=5+√2 an...

Question

If , a=5+√2 and b=1÷a then find the value of a²+b²

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Solution

A=5+2√6, b=1/a=1/(5+2√6)

a²+b²=a²+1/a²
=(5+2√6)²+1/(5+2√6)²
=(25+24+10√2)+1(5-2√6)²/(5+2√6)²(5-2√6)²
=(49+10√2)+(5-2√6)²/(5²-2√6²)
=(49+10√2)+(25+24-10√2)/(25-24)
=(49+10√2)+(49-10√2)/1
=49+10√2+49-10√2
=98

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Similar questions

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{[1 - {(\frac{a}{b})}^{- 2}] a^{2}}{(\sqrt{a} - \sqrt{b})^{2} + 2 \sqrt{a b}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ = 1

a + b = 5,

a

b

a = 2 + \sqrt{5}

b = \frac{1}{a}

a^{2} + b^{2}

a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}

b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}

, then find the value of

\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}

a = \frac{2 - \sqrt{5}}{2 + \sqrt{5}}

b = \frac{2 + \sqrt{5}}{2 - \sqrt{5}}

, then find the value of

a^{2} - b^{2}

a = 2 + \sqrt{5}

b = \frac{1}{a}

a^{2} + b^{2}

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