Question

If x+1/×=sqrt (2) , find (i) x^2+1/x^2 (ii) x^3+ 1/x^3​

Answer 1

Answer:

(i) 0 , (II)-$\sqrt{2}$

Step-by-step explanation:

(a+b)^2 = a^2 + b^2 +2ab

or

a^2 + b^2 = (a+b)^2 - 2ab, this way:

(i) $x^{2} +\frac{1}{x^{2} } = (x + \frac{1}{x} )^{2} -2(x)(\frac{1}{x}) = (\sqrt{2} )^{2} -2=2-2=0$

(a+b)^3 = a^3 + b^3 + 3ab(a+b)

or

a^3 + b^3 = (a+b)^3 - 3ab(a+B)

(ii) $\sqrt{2} ^{3} -3\sqrt{2}$