If x = (7+4√3), then what is the value of x+1/x?
Answers
Answered by
2
Take the value of 1\x =1/7+4√3 and then rationalise it and add both the equations.
Answered by
4
X = 7 + 4√3
1 / X = 1 / 7 + 4 √3
= (7 - 4 √3) / (7 + 4 √3 ) ( 7 - 4 √3 )
= 7 - 4 √3 / 7 ^2 - ( 4 √3 ) ^ 2
= 7 - 4 √3 / 49 - 48
= 7 - 4 √3 / 1 = 7 - 4 √3
X +1 / X = (7 + 4 √3 ) + ( 7 - 4 √3 )
X + 1 / X = 7 ^ 2 - (4 √3 ) ^2
= 49 - 48 = 1
The final answer is 1.
Hope this helps you.☺☺☺
1 / X = 1 / 7 + 4 √3
= (7 - 4 √3) / (7 + 4 √3 ) ( 7 - 4 √3 )
= 7 - 4 √3 / 7 ^2 - ( 4 √3 ) ^ 2
= 7 - 4 √3 / 49 - 48
= 7 - 4 √3 / 1 = 7 - 4 √3
X +1 / X = (7 + 4 √3 ) + ( 7 - 4 √3 )
X + 1 / X = 7 ^ 2 - (4 √3 ) ^2
= 49 - 48 = 1
The final answer is 1.
Hope this helps you.☺☺☺
Similar questions