Question

if x
$if x = 7 + 5 \sqrt{2 } find \: the \: value \: of \: x { }^{2} + 1 \div x {2}$
​

Answer 1

Answer:

Given:

• x = 7 + 5√2

To Find:

• x² + 1/x²

Solution:

⇒ 1/x = 1 / ( 7 + 5√2 )

Rationalising we get,

⇒ ( 7 - 5√2 ) / ( 49 - 50 )

⇒ -7 + 5√2

⇒ x + 1/x = 7 + 5√2 - 7 + 5√2

⇒ x + 1/x = 10√2

⇒ ( x + 1/x )² = x² + 1/x² +  2.x.1/x

⇒ ( x + 1/x )² = x² + 1/x² + 2

⇒ x² + 1/x² = ( x + 1/x )² - 2

⇒ x² + 1/x² = ( 10√2 )² - 2

⇒ x² + 1/x² = 200 - 2

⇒ x² + 1/x² = 198

Hence the value of ( x² + 1/x² ) is 198.

Hope it helped !!

Answer 2

$\huge{\pink{\green {\sf\boxed{ANSWER = 198}}}}$

$\bold{\underline {Given:}}$

$⟹ {x} = {7 + 5} {\sqrt{2}}$

$\bold{\underline {To \:find:}}$

⟹ Value of ${x}^{2} +\dfrac{1}{x}^{2}$

Step-by-step explanation:

$\small {\red{\boxed{For\: full\: solution\: refer \:to\: the \:attached\:pic}}}$

#Be_Brainly