7. Counting by fives, write the numbers from (8723 to 8743 (b) 15910 to 15930
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If a =9-4√5 , find the value of a²+1/a²
a = 9-4√5
1/a = 1/ (9 - 4√5)
= (9 + 4√5) /((9 - 4√5)(9 + 4√5) )
= (9 + 4√5) /(81 - 80)
= (9 + 4√5)
a²+1/a² = (a + 1/a)² - 2a(1/a)
= ( 9 - 4√5 + 9 + 4√5)² - 2
= 18² - 2
= 324 - 2
= 322
or
a²+1/a² = (a - 1/a)² + 2a(1/a)
= ( 9 - 4√5 - 9 - 4√5)² + 2
= (-8√5)² + 2
= 320 + 2
= 322
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