((5+2√6)^2)+(1/5+2√6)^2
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Solution:
(5+2√6)²+1/(5+2√6)²
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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)
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=(5+2√6)²+(5-2√6)²
= 2[2²+(2√6)²]
/*(a+b)²+(a-b)²=2(a²+b²) */
=2[4+24]
= 2×28
= 56
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