Answer question no. 14
after = question is a+b√5
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Hiii friend,
7+✓5/7-✓5 - 7-✓5/7+✓5 = A + B✓5
LHS = 7+✓5/7-✓5 - 7-✓5/7+✓5
=> (7+✓5)(7+✓5) - (7-✓5)(7-✓5)/ ( 7+✓5) (7-✓5)
=> (7+✓5)² - (7-✓5)²/ (7)² - (✓5)²
=> (7)² + (✓5)² + 2 × 7 × ✓5 - { (7)² + (✓5)² - 2 × 7 × ✓5)} / 49 - 5
=> 49 + 5 + 14✓5 - (49+5-14✓5)/ 44
=> 49 + 5 + 14✓5 - 49 - 5 + 14✓5 /44
=> 14✓5 + 14✓5/44
=> 28✓5/44 => 14✓5/22 = 7✓5/11
Now,
LHS = RHS
1+ 7✓5/11 = A+ B✓5
Clearly,
A = 1 and B = 7/11
HOPE IT WILL HELP YOU..... :-)
7+✓5/7-✓5 - 7-✓5/7+✓5 = A + B✓5
LHS = 7+✓5/7-✓5 - 7-✓5/7+✓5
=> (7+✓5)(7+✓5) - (7-✓5)(7-✓5)/ ( 7+✓5) (7-✓5)
=> (7+✓5)² - (7-✓5)²/ (7)² - (✓5)²
=> (7)² + (✓5)² + 2 × 7 × ✓5 - { (7)² + (✓5)² - 2 × 7 × ✓5)} / 49 - 5
=> 49 + 5 + 14✓5 - (49+5-14✓5)/ 44
=> 49 + 5 + 14✓5 - 49 - 5 + 14✓5 /44
=> 14✓5 + 14✓5/44
=> 28✓5/44 => 14✓5/22 = 7✓5/11
Now,
LHS = RHS
1+ 7✓5/11 = A+ B✓5
Clearly,
A = 1 and B = 7/11
HOPE IT WILL HELP YOU..... :-)
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