answer my question
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a^2 =7+4√3
1/a^2=1/7+4√3. ( by rationalising the denominator we will get)
7-4√3
Now,a^2+1/a^2
=7+4√3+7-4√3
=14 ans.
plz mark me as brainliest i need
1/a^2=1/7+4√3. ( by rationalising the denominator we will get)
7-4√3
Now,a^2+1/a^2
=7+4√3+7-4√3
=14 ans.
plz mark me as brainliest i need
Answered by
0
Given,
a = 2 + √3.
So, 1 / a = 1 / ( 2 + √3 )
To rationalize the denominator , multiply the numerator and denominator by ( 2 - √3 ).
1/ a = 1( 2 - √3 ) / ( 2+ √3 ) ( 2 - √3 )
1 / a = ( 2 - √3 ) / { ( 2 )^2 - ( √3 )^2 } [ ( a+b)(a-b)=a^2 - b^2 ]
1 / a = ( 2 - √3 ) / ( 4 - 3 )
1 / a = ( 2 - √3 ) / 1 = ( 2 - √3 ).
Now,
= a^2 + ( 1 / a )^2
By substituting the values of a and 1 / a ,
= ( 2 + √3 )^2 + ( 2 - √3 )^2
= ( 2)^2 + (√3 )^2 + 2 * 2 * √3 + ( 2 )^2 + ( √3 )^2 - 2* 2 * √3
= 4 + 3 + 4√3 + 4 + 3 - 4√3
= 7 + 7
= 14.
So, your final answer is 14.
a = 2 + √3.
So, 1 / a = 1 / ( 2 + √3 )
To rationalize the denominator , multiply the numerator and denominator by ( 2 - √3 ).
1/ a = 1( 2 - √3 ) / ( 2+ √3 ) ( 2 - √3 )
1 / a = ( 2 - √3 ) / { ( 2 )^2 - ( √3 )^2 } [ ( a+b)(a-b)=a^2 - b^2 ]
1 / a = ( 2 - √3 ) / ( 4 - 3 )
1 / a = ( 2 - √3 ) / 1 = ( 2 - √3 ).
Now,
= a^2 + ( 1 / a )^2
By substituting the values of a and 1 / a ,
= ( 2 + √3 )^2 + ( 2 - √3 )^2
= ( 2)^2 + (√3 )^2 + 2 * 2 * √3 + ( 2 )^2 + ( √3 )^2 - 2* 2 * √3
= 4 + 3 + 4√3 + 4 + 3 - 4√3
= 7 + 7
= 14.
So, your final answer is 14.
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