Question

a^2-5a-1=0, find a+1/a,a^2-1/a^2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$a+\frac{1}{a}=\sqrt{29}$

$a^2-\frac{1}{a^2}=5\sqrt{29}$

Step-by-step explanation:

Given : Equation $a^2-5a-1=0$

To find : $a+\frac{1}{a},a^2-\frac{1}{a^2}$

Solution :

Re-write the equation as,

$a^2-1=5a$

$a(a-\frac{1}{a})=5a$

$a-\frac{1}{a}=5$

Taking,  $(a+\frac{1}{a})^2=(a-\frac{1}{a})^2+4a\times \frac{1}{a}$

$(a+\frac{1}{a})^2=(5)^2+4$

$(a+\frac{1}{a})^2=25+4$

$(a+\frac{1}{a})^2=29$

Taking root both side,

$a+\frac{1}{a}=\sqrt{29}$

Taking, $a^2-\frac{1}{a^2}=(a+\frac{1}{a})(a-\frac{1}{a})$

$a^2-\frac{1}{a^2}=(\sqrt{29})(5)$

$a^2-\frac{1}{a^2}=5\sqrt{29}$

#Learn more

Simplify:√(a^2-b^2)+a/√(a^2+b^2)+b ÷√(a^2+b^2)-b/a-√(a^2-b^2)

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