Question

Please help me and do it in paper
If x=3+2√2 find the value of (√x-1/√x)^3

Answer 1

It is given that X=3+2√2

X=√2^2+1^2+2×√2×1

X=(√2+1)^2...........{a^2+b^2+2ab=(a+b)^2}

√x=√{(√2+1)^2}=√2+1

(√x-1/√x)^3

(√2+1-1/√2+1)^3

(√2/√2+1)^3

(√2)^3/(√2+1)^3

2√2/2√2+1+3×2×1+3×√2×1{(a+b)^3=a^3+b^3+3a^2b+3ab^2}

2√2/2√2+3√2+7

2√2/5√2+7(Ans.)

you can also turn into rational denominator if u liked.

Thank you!

pls brainlise me if I am right.