Question

If alpha and beta are real and distinct roots of x^2+1=x/a satisfy mod alpha^2-beta^2>1/a then a belongs to

Answer 1

Step-by-step explanation:

कोठा नंबर ऑफ वैल्यू सॉन्ग

gh

$\sin( \alpha \times 7) 5201522 |5|$

Answer 2

Answer:

a belongs to $- \frac{1}{\sqrt{5} } and \frac{1}{\sqrt{5} }$.

Step-by-step explanation:

$x^{2} +1=\frac{x}{a}\\ or , ax^{2} -x+a=0$

Sum of the roots =$\frac{1}{a}$

multiplication of the roots =  1

$(\alpha ^{2}-\beta ^{2} ) > \frac{1}{a} \\or , (\alpha -\beta )(\alpha +\beta ) > \frac{1}{a}\\or , (\sqrt{\frac{1}{a^{2} }-4 } )(\frac{1}{a} ) > \frac{1}{a}\\or , \frac{1}{a^{2} }-4 > 1\\or , \frac{1}{a^{2} } > 5\\or , a^{2} < \frac{1}{5}\\or , -\frac{1}{\sqrt{5} } < a < \frac{1}{\sqrt{5} }$

a belongs to $- \frac{1}{\sqrt{5} } and \frac{1}{\sqrt{5} }$

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