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| 1. |
If a = 3-√5÷2 find the value of a^2+1÷a^2 |
| Answer» A= (3+√5)/21/a = 1/[(3+√5)/2]=> 1/a = 2/(3+√5)\xa0=> 1/a = 2(3-√5)/(3+√5)(3-√5)rationalizing the denominator=> 1/a = (6-2√5)/3²-(√5)²=> 1/a = (6-2√5)/9-5\xa0=> 1/a = (6-2√5)/4\xa0(a+1/a)² = a²+1/a ²+2=> [(3+√5)/2 + (6-2√5)/4] = a²+1/a²+2=> [2(3+√5)/(2)2 + (6-2√5)/4] = a²+1/a²+2Making denominator equal=> (6+2√5+6-2√5)/4 = a²+1/a²+2=> 12/4 = a²+1/a²+2=> 3 = a²+1/a²+2=> 3-2 = a²+1/a²=> 1 = a²+1/a² | |