Question

x=1/3+2√2 then find the value of x²+1/x²​

Answer 1

$\huge\boxed{\texttt{\fcolorbox{purple}{pink}{Heya !!!}}}$

FIRSTLY,

WE KNOW

$x = 1 \div (3 + 2 \sqrt{2} )$

LET'S RATIONALISE IT,

$x =( 1 \div (3 + 2 \sqrt{2} ) )\times( (3 - 2 \sqrt{2} ) \div (3 - 2 \sqrt{2} ))$

$x = (3 - 2 \sqrt{2} ) \div (9 - 6 \sqrt{2} + 6 \sqrt{2} - 8)$

$x = (3 - 2 \sqrt{2} ) \div 1$

NOW LET'S SQUARE x...

${x}^{2} =( 3 - 2 \sqrt{2} ) {}^{2}$

$x {}^{2} = 9 - (4 \times 2)$

$x {}^{2} = 9 - 8 = 1$

THEREFORE,

$1 \div {x}^{2} = 1 \div 1$

LET'S NOW FIND x^2+1/x^2...

i.e. 1+(1÷1)=2


HOPE IT HELPS YOU...


HIT❤
MARK BRAINLIEST AND FOLLOW ME...

THANKS♥❤♥