Math, asked by atharvk8, 2 months ago

if a= 2+√5 and b=1\a then find a^+ b^​

Answers

Answered by Anonymous
0

Answer:

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Answered by akankshadhankar
0

18 is answer

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

5

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

a

1

so,

b = \frac{1}{2 + \sqrt{5} }b=

2+

5

1

b = \frac{1 \times( 2 - \sqrt{5} )}{2 + \sqrt{5} \times (2 - \sqrt{5}) }b=

2+

5

×(2−

5

)

1×(2−

5

)

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

2

2

−5

2−

5

b = \frac{2 - \sqrt{5} }{4 - 5}b=

4−5

2−

5

b = \frac{2 - \sqrt{5} }{ - 1}b=

−1

2−

5

b = \sqrt{5 } - 2b=

5

−2

{a}^{2} + {b}^{2}a

2

+b

2

so put value of a and b in eq.

{(2 + \sqrt{5} )}^{2} + { (\sqrt{5 } - 2)}^{2}(2+

5

)

2

+(

5

−2)

2

we. get

{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2b(a+b)

2

=a

2

+b

2

+2b

(4 + 5 + 2(4)( \sqrt{5} )\: \: + (4 + 5 +( - 2 \times 4 \times \sqrt{5} ))(4+5+2(4)(

5

)+(4+5+(−2×4×

5

18

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