If x-1/x=4,then find the value of x2+1/x2

1.	If x-1/x=4,then find the value of x2+1/x2
Answer» GIVEN:- $\rm{x-\dfrac{1}{x}=4}$ TO FIND:- $\rm{x^2+\dfrac{1}{x^2}}$ IDENTITY USED:- $\rm{(a-b)^2=a^2-2ab+b^2}$ Now, $\implies\rm{x-\dfrac{1}{x}=4}$ Squaring the both SIDES. $\implies\rm{(x-\dfrac{1}{x})^2=(4)^2}$ $\implies\sf{x^2+\dfrac{1}{x^2}-2\times{\cancel{x}}}\times{\dfrac{1}{\cancel{x}}}=16}$ $\implies\rm{x^2+\dfrac{1}{x^2}-2=16}$ $\implies\rm{x^2+\dfrac{1}{x^2}=18}$ . HENCE, The value of $\rm{x^2+\dfrac{1}{x^2}}$ is 18. SOME MORE IDENTITY. $\rm{(a+b)^2=a^2+2ab+b^2}$ $\rm{a^3+b^3=(a+b)(a^2-ab+b^2)}$ $\rm{a^3-b^3=(a-b)(a^2+ab+b^2)}$

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