Question

if x=1-root2 find x square+1/x square

Answer 1

Step-by-step explanation:

x = 1 - √2

x² + 1 / x² = ?

1 / x = 1 / 1 - √2

= 1 / 1 - √2 * 1 + √2 / 1 + √2

= 1 + √2 / -3

( x + 1 / x )² = x² + 1 / x² + 2 * x * 1 / x ( x and 1 / x will be cut )

( 1 + √2 + ( 1 + √2 / 3 ))² = x² + 1 / x² + 2

x² + 1 / x² = ( 3 + 3√2 + 1 + √2 / 3 )² - 2

= ( 4 + 4√2 )² - 2

= 16 + 32 + 2 * 4 * 4√2 - 2

= 56 + 32√2

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Answer 2

x= 1-√2 ( given)

x²+1

-------- = find

x²

x+1 1-√2+1

----- = --------------

x 1-√2

2-√2

-------- Rationalising the value

1-√2

2-√2. 1+√2. 2(1+√2)-√2(1+√2)

------- × -----------. = -----------------------------

1-√2. 1+√2. (1)²-(√2)²

2+2√2-√2-2. √2

-------------------. = ------

1-2. -1

x+1/x=-√2

squaring both sides,

(x+1)²

--------. = 2

x²

x²+1+2x

------------- =2

x²

x²+1

-------- = 2-2(1-√2)

x²

x²+1

-------- =2-2+2√2

x²

x²+1

-------- = 2√2

x²

hope it works out for you!!!