If x=3+2√2, what is the value of √x -1/√x?
Solution
Correct Answer: Option B
এখানে ,
x =3 +2√2
বা,x=2+2√2+1
বা,x=(√2)²+2√2+(1))²
বা,x=(√2+1)²
অতএব , 1/√x =1/(√2+1)
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/(√2)² -(1))²
=(√2-1)/2-1
=(√2-1)/1
=(√2-1)
অতএব ,√x -1/√x = √2+1 -(√2-1)
=√2+1 -√2-1
=2
x =3 +2√2
বা,x=2+2√2+1
বা,x=(√2)²+2√2+(1))²
বা,x=(√2+1)²
অতএব , 1/√x =1/(√2+1)
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/(√2)² -(1))²
=(√2-1)/2-1
=(√2-1)/1
=(√2-1)
অতএব ,√x -1/√x = √2+1 -(√2-1)
=√2+1 -√2-1
=2
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