Question

If x= 3+2√2 then value of x² - 6x +1 is​

Answer 1

Step-by-step explanation:

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Answer 2

GIVEN:-

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

TO FIND:-

The Value of x²-6x+1.

Now

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

$\implies\rm{x=3+2\sqrt{2}}$

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

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

$\implies\rm{x^{2}=9+12\sqrt{2}+8}$

$\implies\rm{x^{2}=17+12\sqrt{2}}$.

Now,

$\implies\sf{x^2-6x+1}$

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

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

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

$\implies\sf{17-18+1}$

$\implies\sf{-1+1}$

$\implies\sf{0}$

Hence, the value of x² - 6x +1 is 0