Saved Bookmarks
| 1. |
If a=3-2√2, find a ²-1/a^2 |
|
Answer» Answer: 34 Step-by-step EXPLANATION: Given-----> a = 3 - 2√2 To find----> a² - 1 / a² Solution-----> ATQ,
a = 3 - 2√2 1 / a = 1 / ( 3 - 2√2 ) Multiplying by ( 3 + 2√2 ) in NUMERATOR and denominator we get, = ( 3 + 2√2 ) / ( 3 - 2√2 ) ( 3 + 2√2 ) We know that, a² - b² = ( a + b ) ( a - b ) , we get, = ( 3 + 2√2 ) / { ( 3 )² - ( 2√2 )² } = ( 3 + 2√2 ) / ( 9 - 8 )
= ( 3 + 2√2 ) / 1 => 1/a = ( 3 + 2√2 ) Now , a = ( 3 - 2√2 ) Squaring both sides , we get, => a² = ( 3 - 2√2 )² We know that, ( a - b )² = a² + b² - 2ab , applying it we get, = ( 3 )² + ( 2√2 )² - 2 ( 3 ) ( 2√2 ) = 9 + 8 - 12√2 => a² = 17 - 12√2 Now, 1 / a = 3 - 2√2 Sqaring both sides we get, => 1 / a² = ( 3 + 2√2 )² We know that , ( a + b )² = a² + b² + 2ab , we get, = ( 3 )² + ( 2√2 )² + 2 ( 3 ) ( 2√2 ) = 9 + 8 + 12√2 => 1 / a² = 17 + 12√2 Now, a² + 1 / a² = ( 17 - 12√2 ) + ( 17 + 12√2 ) = 34 |
|