Question

if x= 3+2√ 2 then find x+1/x​

Answer 1

Answer:

Step-by-step explanation:

√x)-(1/√x))^2=x+(1/x)-2*x*(1/x).I.e

(a-b)^2=a*a+b*b-2*a*b.

((√x)-(1/√x))^2=(3–2√2)+(1/3–2√2)-2*(3–2√2)*(1/3–2√2).

Rationalising the above factor (3–2√2) I.e

Multiplying with (3+2√2) in numerator and denominator.so the result be (3+2√2).

((√x)-(1/√x))^2=(3–2√2)+(3+2√2)-2.

((√x)-(1/√x))^2=3+3–2=4.

Applying square root on both sides

(√x)-(1/√x)=2.

So the answer is 2.

Answer 2

$\frac{3 + 2 \sqrt{2} + 1}{3 + 2 \sqrt{2} } \\ = \frac{(4+ 2 \sqrt{2}) }{(3 + 2 \sqrt{2}) } \times \frac{(3 - 2 \sqrt{2} )}{(3 - 2 \sqrt{2}) } \\ = \frac{12 - 8 \sqrt{2} + 6 \sqrt{2} - 8 }{ ({3})^{2} - {(2 \sqrt{2}) }^{2} } \\ = \frac{4 - 2 \sqrt{2} }{9 - 8} \\ = 4 - 2 \sqrt{2}$