FIND x-1/x, if x=3+2√2
Answers
Answer:
Step-by-step explanation:
SIMILAR ANSWER HERE BUT SIGNS ARE INTERCHANGED
Given, x =3-2√2
We have to find the value of x+(1/x)
Taking lcm,
x+(1/x) = (x²+1)/x
Replacing the value of x
= {(3-2√2)²+1}/3-2√2
{(3-2√2)²} can be written as (3-2√2)(3-2√2) for our convenience
= {(3-2√2)(3-2√2)+1}/3-2√2
By rationalizing,
= [{(3-2√2)(3-2√2)+1}/3-2√2] × [3+2√2/3+2√2]
= [(3+2√2)(3-2√2)(3-2√2) + 1(3-2√2)] / (3-2√2)(3+2√2)
We know that (3-2√2)(3-2√2) = 9-8 = 1
Placing it in (3+2√2)(3-2√2)
= 1(3-2√2)+1(3-2√2)/1
= 3-2√2+3-2√2
= 3+3
= 6
therefore, the value of x+(1/x) = 6
Read more on Brainly.in - https://brainly.in/question/344560#readmoreGiven, x =3-2√2
We have to find the value of x+(1/x)
Taking lcm,
x+(1/x) = (x²+1)/x
Replacing the value of x
= {(3-2√2)²+1}/3-2√2
{(3-2√2)²} can be written as (3-2√2)(3-2√2) for our convenience
= {(3-2√2)(3-2√2)+1}/3-2√2
By rationalizing,
= [{(3-2√2)(3-2√2)+1}/3-2√2] × [3+2√2/3+2√2]
= [(3+2√2)(3-2√2)(3-2√2) + 1(3-2√2)] / (3-2√2)(3+2√2)
We know that (3-2√2)(3-2√2) = 9-8 = 1
Placing it in (3+2√2)(3-2√2)
= 1(3-2√2)+1(3-2√2)/1
= 3-2√2+3-2√2
= 3+3
= 6
therefore, the value of x+(1/x) = 6
#LOVE #SAY THANKS TO APPRECIATE
Answer:
Step-by-step explanation: solution is given below
