Question

If x=3 +2V2 then value of xsquare- 6x + 1​

Answer 1

Answer:

GIVEN:-

If \rm{x=3+2\sqrt{2}}x=3+2

2

TO FIND:-

The Value of x²-6x+1.

Now

We will first Rationalisation the value of x and will find x².

\implies\rm{x=3+2\sqrt{2}}⟹x=3+2

2

\implies\rm{(x)^2=(3+2\sqrt{2})}⟹(x)

2

=(3+2

2

)

\implies\rm{x^{2}=3^2+2\times{3}{2\sqrt{2}}+(2\sqrt{2})^2}⟹x

2

=3

2

+2×32

2

+(2

2

)

2

\implies\rm{x^{2}=9+12\sqrt{2}+8}⟹x

2

=9+12

2

+8

\implies\rm{x^{2}=17+12\sqrt{2}}⟹x

2

=17+12

2

.

Now,

\implies\sf{x^2-6x+1}⟹x

2

−6x+1

\implies\sf{17+12\sqrt{2}-6(3+2\sqrt{2})+1}⟹17+12

2

−6(3+2

2

)+1

\implies\sf{17+12\sqrt{2}-18-12\sqrt{2}+1}⟹17+12

2

−18−12

2

+1

\implies\sf{17+\cancel{12\sqrt{2}}-18-\cancel{12\sqrt{2}}+1}⟹17+

12

2

−18−

12

2

+1

\implies\sf{17-18+1}⟹17−18+1

\implies\sf{-1+1}⟹−1+1

\implies\sf{0}⟹0

Hence, the value of x² - 6x +1 is 0