If a is equal to 5-2root 5 find a square - 1/a square
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Here,
a = 5 + 2√6
b = 1/a
=1/( 5 + 2√6)
=(5 -2√6)/(5+2√6)(5 -2√6)
=(5 -2√6)/{5² -(2√6)²}
=(5 -2√6)/(25 -24)
=5 -2√6
now,
a² + b² = (a + b)² -2ab
=(5 +2√6 +5 -2√6)² -2(5 +2√6)(5 -2√6)
=(10)² -2(25 -24)
=100 -2
= 98
hence, a² + b² = 98
a = 5 + 2√6
b = 1/a
=1/( 5 + 2√6)
=(5 -2√6)/(5+2√6)(5 -2√6)
=(5 -2√6)/{5² -(2√6)²}
=(5 -2√6)/(25 -24)
=5 -2√6
now,
a² + b² = (a + b)² -2ab
=(5 +2√6 +5 -2√6)² -2(5 +2√6)(5 -2√6)
=(10)² -2(25 -24)
=100 -2
= 98
hence, a² + b² = 98
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