Question

If x-1/x =12,then find the value of x ²-1/x²

Answer 1

Answer:

$x-\frac{ 1}{x} =12\\(x-\frac{ 1}{x} )^2=(12)^2\\x^{2}-2(x)(\frac{ 1}{x} )+(\frac{ 1}{x} )^2=144\\x^{2}+ \frac{ 1}{x ^2} -2=144\\x^{2}+ \frac{ 1}{x ^2} =146\\\\and\\(x+ \frac{ 1}{x })^2=x^{2}+ \frac{ 1}{x ^2}+2 (x)(\frac{ 1}{x} )\\(x+ \frac{ 1}{x })^2=146+2\\(x+ \frac{ 1}{x })^2=148\\x+ \frac{ 1}{x }=\sqrt{148} \\then\\ x^{2} -\frac{1}{ x^{2}} =(x+\frac{1}{ x })(x-\frac{1}{ x })\\ x^{2} -\frac{1}{ x^{2}} =\sqrt{148}(12)=24\sqrt{37}$