I am not understanding the last step in the solution of x^2+2x+3 in pdf

1
Have you understood up to (x+1)^2+(√2)^2 ? So that I can continue from there
Answer given in the book isn't right.
you tell me from (x+1)^2+(√2)^2 plz explain
but wr to answer
its a little printing mistake '+' should be kept after 3 in first bracket

Answers

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2014-11-04T13:47:28+05:30

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X²  + 2x + 3
= x² + 2x + 1 + 2
=(x+1)² + 2
=(x+1)² + (√2)²
I hope you understood till that point.

Now what the book has done is:
you can expand a⁴ + b⁴ as
a⁴ + b⁴ = a⁴ + b⁴ + 2a²b² - 2a²b²
          = (a²)² + 2.a².b² + (b²)² - 2.a².b²
          = ( a² + b² )² - 2.a².b²
          = ( a² + b² )² - (√(2.a².b²))²
you know x² - y² = (x+y)(x-y)
So a⁴ + b⁴ = [ ( a² + b² ) + (√(2.a².b²)) ] [ ( a² + b² ) - (√(2.a².b²)) ]

In the question,
a⁴ = (x+1)²     
⇒a² = (x+1) and
b⁴ = (√2)²
⇒ b² = √2

Putting in the formula 

 (x+1)^{2} +(  \sqrt{2} )^{2} =[(x+1)+ \sqrt{2}+ \sqrt{2(x+1) \sqrt{2} } }\  \  ]*[(x+1)+ \sqrt{2}- \sqrt{2(x+1) \sqrt{2} } }\ \ ]

(x+1)^{2} +( \sqrt{2} )^{2} =[x+1+ \sqrt{2}+ \sqrt{2 \sqrt{2} (x+1)} }\ \ ]*[x+1+ \sqrt{2}- \sqrt{2 \sqrt{2} (x+1)} }\ \ ]

The answer in the book is wrong. you can check by multiplying that.
2 5 2
If you have still any doubt,leave a comment. i will get back to you.