Express x-x2-13-x-x2-13 as a polynomial in x-

Now, (x+√(x^2+1))^3+(x √(x^2+1))^3 =(x+√(x^2+1)+x √(x^2+1))^3 3(x+√(x^2+1))(x √(x^2+1))(x+√(x^2+1)+x √(x^2+1)) =8x^3 3.( 1).2x =8x^3+6x . ...

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Byju's Answer

Standard IX

Mathematics

Polynomial and Its General Form

Express x+√...

Question

Express ${(x + \sqrt{x^{2} + 1})}^{3} + {(x - \sqrt{x^{2} + 1})}^{3}$ as a polynomial in $x$ .

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Solution

Now,
${(x + \sqrt{x^{2} + 1})}^{3} + {(x - \sqrt{x^{2} + 1})}^{3}$
$= (x + \sqrt{x^{2} + 1} + x - \sqrt{x^{2} + 1})^{3} - 3 (x + \sqrt{x^{2} + 1}) (x - \sqrt{x^{2} + 1}) (x + \sqrt{x^{2} + 1} + x - \sqrt{x^{2} + 1})$
$= 8 x^{3} - 3. (- 1) .2 x$
$= 8 x^{3} + 6 x$ .

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Express (x+√x2+1)3+(x−√x2+1)3 as a polynomial in x.

Now,(x+√x2+1)3+(x−√x2+1)3=(x+√x2+1+x−√x2+1)3−3(x+√x2+1)(x−√x2+1)(x+√x2+1+x−√x2+1)=8x3−3.(−1).2x=8x3+6x.

Express ${(x + \sqrt{x^{2} + 1})}^{3} + {(x - \sqrt{x^{2} + 1})}^{3}$ as a polynomial in $x$ .

Now,
${(x + \sqrt{x^{2} + 1})}^{3} + {(x - \sqrt{x^{2} + 1})}^{3}$
$= (x + \sqrt{x^{2} + 1} + x - \sqrt{x^{2} + 1})^{3} - 3 (x + \sqrt{x^{2} + 1}) (x - \sqrt{x^{2} + 1}) (x + \sqrt{x^{2} + 1} + x - \sqrt{x^{2} + 1})$
$= 8 x^{3} - 3. (- 1) .2 x$
$= 8 x^{3} + 6 x$ .