if ✓x-1/x^2 =5 then find value of x^2+1/x^2
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[math]x^2-(\dfrac{1}{x})^2=(x+\dfrac{1}{x})(x-\dfrac{1}{x})[/math]
We know that [math]\:(a+b)^2=(a-b)^2+4ab[/math]
Hence, [math]\:(x+\dfrac{1}{x})^2=(x-\dfrac{1}{x})^2+4\cdot x\cdot \dfrac{1}{x}=25+4=29[/math]
Hence the required solution is [math]\:\pm 5\sqrt {29}[/math]
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