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Algebra Level 1

If $x^2 - \dfrac1{x^2} = 100$ , what is the relationship between the two numbers,

$\left( x + \dfrac1x\right) \ \text{ and } \ \left( x - \dfrac1x \right) \; ?$

Their sum is 100 Their absolute difference is 100 Their product is 100 Their ratio is 100

2 solutions

Khang Nguyen Thanh
Mar 15, 2016

$x^2-\dfrac{1}{x^2}=\left(x-\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}\right)$

Stephen Liado
Mar 21, 2016

Recall that x^2-y^2=(x+y)(x-y)

So:

x^2-1/x^2 =100 (x)^2-(1/x)^2=100 (x+1/x)(x-1/x)=100

Therefore, their product is 100.