If a=2+√5 and b= 1/a
then find a² + b²
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Answered by
1
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
))
(4 + 5 + 8 \sqrt{5} ) + (4 + 5 - 8 \sqrt{5} )(4+5+8
5
)+(4+5−8
5
)
9 + 99+9
18 ans
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