Question

If x = (3+under root 8), show that (x square +1/x sq ) =34

Answer 1

Step-by-step explanation:

x=3+√8 =3+√2×2×2 =3+2√2.

1/x = 1/(3+2√2) =(3-2√2)/(3-2√2)(3+2√2) =

(3-2√2)/(9-8) = 3-2√2.

x+ 1/x =>3+2√2+3-2√2 =>6. Square on both sides we get

${(x + \frac{1}{x})}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = >$

${6}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 = > 36 - 2 = 34 =$

${x}^{2} + \frac{1}{ {x}^{2}}$

Hence Showed. Hope it helps you.